JP2007188462A - Method of displaying volumetric 3d image - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of displaying physiological and mental depth cues on a volumetric 3D display. <P>SOLUTION: A fundamental concept is that distorted coordinate systems are combined in order to display both a physiological depth cue and a great mental depth cue of the volumetric 3D display, and a volume of the display includes two parts of a physical 3D space and a virtual space in a 2D screen. That is, an object to be displayed is displayed as a volumetric 3D image in accordance with distorted 3D coordinates when being within the physical 3D space, and the object is displayed as a background by a perspective drawing of the 2D screen when being beyond the physical 3D space within the virtual space. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

The present invention relates to the following patents and applications to the applicant:
US Patent 5,754,147,
US Patent 5,954,414,
US Pat. No. 6,302,542 B1,
US Pat. No. 6,765,566B1,
US Pat. No. 6,961,045B1,
US Patent Application Publication 2005-0280605-A1,
Japanese Patent Application 361090/99 (Domestic Patent Application Notification 2000/201362),
Japanese Patent Application 2001/318189 (Domestic Patent Application Notification 2002/268136),
Japanese Patent Application 2002/175379 (Domestic Patent Application Notification 2003/107399),
Applicant has incorporated the above document as a cited reference in this case.

      The present invention relates to the field of volumetric 3D displays. Among other things, it relates to the display of volumetric 3D images of large psychological visual depth colors.

      The volumetric 3D display displays the real 3D space of the 3D image. Each “voxel” in the volume image is actually and physically located at the expected spatial location, and the rays travel directly from that location in all directions to view the actual image Form on the eyes. As a result, volumetric 3D images possess all the major elements in both physiologic and psychological depth cues, and are viewed around multiple viewers without the need for special glasses. Of 360 degrees.

      There are many different approaches to volumetric 3D displays. One department uses a mobile display panel. The moving display panel distributes a frame of 2D image in space to form a volumetric 3D image by the afterimage effect. For example, Bcrlin US Pat. No. 4,160,973 describes a system with a panel of rotating LEDs that sweeps the volume of a cylindrical display. As another example, Tsao Japanese Patent Application Notice 2002/268136 (FIG. 11) describes a system with a “rotary reciprocating” display panel. The flat panel display rotates with a surface that always faces in a fixed direction about the axis. As a result, the display panel sweeps in a reciprocating manner in the display space.

      Another department of volumetric 3D displays uses moving screens and projects 2D images onto the screen. For example, Tsao Japanese Patent Application Notice 2002/268136 (FIGS. 2a, 4a-4d, 5b) describes a system with a “rotary reciprocating” screen and an optical projector. This is also described in Tsao US Pat. No. 6,765,566 (FIG. 20) and Tsao US Pat. No. 6,302,542 (FIGS. 2a, 4a-4b and 5b). For another example, Tsao US Pat. No. 6,765,566 (FIGS. 14-15) describes a system based on a rotating screen (also in Japanese Patent Application Notice 2000/201362). Other examples include: Batchko US Pat. No. 5,148,310, Shimada US Pat. No. 5,537,251, and Dorval et al. US Pat. No. 6,554,430. Blundell US Pat. No. 5,703,606 describes another type of moving screen system. It uses a moving screen that is coated with phosphor and uses a stationary electron gun to generate an image on the screen.

      Another department uses a stack of display panels (usually liquid crystal displays) as the display volume. Examples are described by Leung and Ives US Pat. No. 5,745,197 and Hattori et al. Optical Engineering, 1992, Vol. 31 second, p. 350 etc. are included.

      Another category uses electrically switchable screens (usually liquid crystal) and optical projector stacks. Examples include Sullivan US Pat. No. 6,100,862 and Sadovnik and Rizkin US Pat. No. 5,764,317.

      Yet another department uses a volume of material that has the properties of "fluorescent step-by-step stimulation" (or commonly referred to as "2-stage stimulation"). Examples are Korevaar US Pat. No. 4,881,068 and Downing et al., Science, Aug. 30, 1996, Vol. 273, p. 1185 is included.

      Applicant has incorporated the above document as a cited reference in this case.

      One problem with the image quality of volumetric 3D displays is the psychological visual depth limit. There is a finite size in the display space, so the physiological visual depth is limited. In contrast, 2D displays can basically display infinite depth of view with psychological depth cues in the form of perspective views.

      Another problem with volumetric 3D displays is the limit of gray (or color) levels. In many volumetric 3D displays based on projections, the preferred source of images for the projector is the DMD (Digital Micromirror Device) or FLCD (Ferroelectric Liquid Crystal Display). These are black and white pixel devices. In order to create colors, we can use three DMD or FLCD panels, each panel illuminated by light of another primary color. Instead, Tsao US Pat. No. 6,961,045 (also in national patent application notice 2003/107399) describes how to use a single panel to generate colors. A single panel is divided into three sub-panels, each sub-panel illuminated by a different primary color light. The three sub-panel images are then recombined into one of the projections. However, since each pixel has only two levels (white and black), a combination of three panels or sub-panels can generate only a limited amount of color.

      The present invention describes a method for displaying physiological and psychological depth cues on a volumetric 3D display. This additional psychological visual depth can display an infinite depth background. It is useful for applications such as flight simulation or electronic games. The invention also describes a method for displaying a high level volumetric 3D image in color or gray scale. The present invention also describes the basic geometric shape rendering principles and algorithms. These principles and algorithms are used to display volumetric 3D images and backgrounds of infinite depth colors.

      To display both the physiological depth cues and the large psychological depth cues of volumetric 3D displays, the basic concept is to combine the skewed coordinate system with a 2D screen. Thus, the volume of the display includes two parts: the physical 3D space and the virtual. space. If the property to be displayed is in a physical 3D space, the property is displayed as a volumetric 3D image according to skewed 3D coordinates. The property is a virtual. If there is any space beyond and beyond the physical 3D space, it will be displayed by the perspective view of the 2D screen as background.

      There are three preferred ways to display images on a 2D screen. The first method is a 2D screen display image as a planar volumetric 3D image. That is, this is a display image of a perspective view of a 2D plane in a 3D volume. Basically, this first method can be applied to all types of volumetric 3D displays. The 2D screen can be placed at any position and orientation of the display volume. The second method displays a 2D image of a perspective view by overlaying a plurality of image frames. The third method uses another projector to generate a perspective image on a 2D screen.

      The high color (or gray) level display image describes a rendering method of the basic geometric shape of the high color level (referred to for convenience as a “geometric base”). The basic concept is to control the ratio of the number of drawn display elements with respect to the total number of display elements in the geometric primitive. The display element is a basic element of the display image in the volume 3D space. The number of drawn display elements represents the desired level of brightness. The total number of display elements represents the highest luminance level. There are two approaches to achieve this control: “point-based rendering” and “intersection-based rendering”.

      In point-based rendering, the sample points were first calculated to represent the geometric basis, and then the sample points were drawn. That is, displaying the geometric basis is displaying sample points. Thus, there is no need to calculate the intersection of geometric primitives and slice frames. Each sample point generally corresponds to the position of one display element. However, the size of the image of the sample points can be adjusted by dilating the points to adjacent display elements. That is, the expansion of a point is a mapping from a single sample point to multiple display elements. In general, the luminance level of a geometric base is proportional to the number of displayed display elements. If the display element itself has a gray scale function, the brightness level is also proportional to the brightness scale of the display element. The total number of rendered display elements can be controlled to give the desired visual brightness by controlling the spatial distribution and size of the sample points.

      In intersection-based rendering, geometric primitives and frame crossings are drawn. In general, each intersection is a small bitmap that contains the pixels of the frame. Stitching all small bitmaps of intersection together forms a conceptual “composite bitmap”. The desired brightness level is then expressed by controlling the ratio of the number of pixels rendered relative to the total number of pixels in the composite bitmap. The small bitmap is then redrawn by the inverse mapping from the composite bitmap being drawn. The redrawn small bitmap then forms a geometric base at the desired brightness level.

In the first method of displaying an image on a 2D screen, the texture mapping method is applied. The perspective background is stored first on the computer as a bitmap (or other similar format). The 2D screen is then rendered as a texture map by using this bitmap. The basic procedure for drawing a monochromatic texture mapping surface is as follows:
(1) Divide the full intensity scale of the texture map into a number of different intensity ranges. Thus, each intensity range corresponds to a different region of the texture map.
(2) Establish a mapping from each region of the texture map to the corresponding region on the surface.
(3) Assign a brightness level to each corresponding area on the surface based on the intensity range of that area according to the mapping.
(4) Draw corresponding areas of different density surfaces of the display element to represent different brightness levels. Point-based rendering is the preferred method. Basically, each corresponding area of the surface is drawn under a mesh system that gives the desired brightness to the entire surface, but the sample points are placed only within the corresponding area.

Large psychological visual depth display

      To display both the physiological depth cues and the large psychological depth cues of volumetric 3D displays, the basic concept is to combine the skewed coordinate system with a 2D screen. Thus, the volume of the display includes two parts: the physical 3D space and the virtual. space. If the property to be displayed is in a physical 3D space, the property is displayed as a volumetric 3D image according to skewed 3D coordinates. Both the location and size of the property should be displayed according to a skewed coordinate system. The property is a virtual. If there is any space beyond and beyond the physical 3D space, it will be displayed by the perspective view of the 2D screen as background.

      FIG. 1 illustrates an example of a skewed coordinate system. The space defined between the plane OPQR and the plane ABCD is a right-angle 3D space with a skewed dimension. The straight line BC has the same length as the straight line PQ, but is shown to amplify the distance to provide a cue with a shorter or psychological depth than the PQ. Thus, the plane ABCD has actually the same area as the plane OPQR, but is shown smaller. Therefore, the space delimited by OPQR and ABCD is a “distorted space”. The plane ABCD is a 2D screen. Properties outside the skewed space and beyond the plane ABCD are virtual. The “inside” of the space. This virtual. There is a virtual 3D coordinate system in space. Virtua. Space properties are displayed according to this virtual 3D coordinate system. Therefore, this 2D screen can display an infinite depth background. The two coordinate systems, the virtual coordinate system and the skew coordinate system are connected by a plane ABCD. As a result, an object such as an airplane image can move smoothly between two spaces, one virtual and one physical. The plane appears to be larger when close to the 0PQR plane. It moves much more when moving from the plane of OPQR towards the plane ABCD and becomes smaller in size due to the skewed coordinate system. So it seems to move farther into space. When an airplane moves inside a 2D screen, it can basically follow an infinite depth. Naturally, the visual effect is most suitable for viewing from the plane OPQR to ABCD.

      FIG. 2 provides a geometric analysis of the coordinate system mapping. A rectangle JKCL represents a side view of the display space of the volumetric 3D display. Virtua. The 2D screen for displaying the space is selected by the “bottom” of the display space, KC. The reference position O is set as the eye position of the distance OB on the 2D screen. A geometric analysis is made because the graph is symmetric on one side of the centerline OB.

First, place a reference plane bb ′ of size W at a distance Ob from the eye in a non-distorted coordinate system. Then, from the position O, do the same for the size of the 2D screen BC and the size of the reference plane bb ′. The relationship between W and Ob is as follows:
BC / W = OB / Ob (001)

      The hypothesis CQ is a straight line, and the coordinate system mapping is the mapping between the rectangular space Pbb'Q and the skewed space PBCQ, and the space above the plane bb 'and the 2D screen BC virtual. Mapping between spaces.

ff ′ is a plane of size W at the distance of Of from the eye position (Of <Ob). According to the mapping of the coordinate system, the position and size FF ′ of the corresponding plane of the skew coordinate system can be obtained.
From the triangle Off '
OF / Of = FF ′ / W. (002)
From the triangle LCQ,
BF / BP = (FF'-PL) / (PQ-PL)
(OB-OF) / BP = (FF'-PL) / (W-PL) (003)
OF and FF 'can be obtained from equations (002) and (003) as a function of Of and other known quantities. That is, it appears that the f size FF ′ image and the f image ff ′ are the same size.

hh ′ is a plane of size W at a distance Oh from the eye position (Oh> Ob). According to the mapping of the coordinate system, the corresponding plane size BH ′ of BC can be obtained. From the triangle Ohh '
BH '/ W = OB / Oh (004)

The mapping between the points in plane ff ′, 450, and the corresponding points in plane FF ′, 451, is as follows:
Fn / fm = FF ′ / W (005)
The same principle applies to the mapping between plane hh ′ and plane BH ′, and accordingly, points in non-distorted space beyond the plane of PQ map mapping points in skewed space PBCQ or in 2D screens. Can be found.

      There are three preferred methods of displaying a 2D screen image. The first method displays a 2D screen image as a planar volumetric 3D image. That is, this is an image display of a perspective view of a 2D plane in a 3D volume. The texture mapping method is an application. The perspective image is first stored on the computer as a bitmap (or other similar format). The 2D screen is then rendered as a texture map by using this bitmap. The texture mapping method is described later.

      The second method displays a 2D image of a perspective view by overlaying a plurality of image frames. On a volumetric 3D display based on a “rotary reciprocating” screen (or display panel), multiple frames can be placed in a limited space when the screen is near the bottom (or top) position. This can increase the color or gray level of the 2D screen. FIG. 3 illustrates the idea. Since the actual track of the moving screen 570 is a circle and the vertical spacing between two adjacent frames is generally uniform, the angle of rotation from one frame to the next is always changing. When the screen is near the bottom, the angle of rotation between two adjacent frames, eg 580c and 580d, is much larger than that near the middle position, eg 580a and 580b. That is, the time between two adjacent frames is much longer when the screen is near the lowest position (or above) because the screen rotates at a constant speed. Thus, the frame can be displayed with a smaller vertical pitch. For example, the additional frame 550 can be inserted between the original frame positions 590d-590f. More color or gray levels can be displayed because more image frames are used to generate a 2D image. The 2D screen can still be displayed by texture mapping. Alternatively, the deadline of the frame near the bottom can be chosen to have a ratio. As a result, different frame pixels have different brightness due to different frame deadlines. This difference in brightness can increase the level of brightness. For example, if three frames are used with a luminance ratio of 1: 2: 4, then there will be eight (0-7) luminance levels instead of each pixel 3 in the superimposed 2D image. This is similar to the method of pulse-width adjustment in Hornbeck US Pat. No. 5,280,277, incorporated herein by reference.

      The third method uses another projector to generate a perspective image on a 2D screen. This method uses a system based on a moving screen in a volumetric 3D display. FIG. 4 illustrates a preferred embodiment. Projector beams from another 2D projector 601 and the original projector 15 are brought by the use of a reflector 602 switchable to the projection path 102. One example of a switchable reflector is an electrically switchable mirror based on liquid crystals. It is described in SID International Symposium 1985, incorporated herein by reference. 16, p. 345. When the screen moves to a 2D screen position, a switchable reflector is made reflective so that the second projector 601 projects a 2D image. When the screen moves into a skewed space, the switchable reflector is made transparent so that only the image from the original projector 15 enters the projection path 102.

      In general, skewed physical space and virtuals. The method of joining the 2D planes of space can be applied to all forms of volumetric 3D displays. The position of the eye reference must be above the middle of the display space. It can be offset from the centerline if necessary when mapping is done accordingly. Furthermore, the 2D screen can be placed in any desired position at the bottom of the display space. For example, FIG. 5 illustrates a 2D screen YB placed away from the bottom plane KC. The principle of spatial mapping is the same. The reference plane Zb is selected. When viewed from position O, the reference plane and the 2D screen YB appear to have the same size. The mapping of the coordinate system includes mapping between the space XZbP and the skewed space XYBP, and the space beyond the plane Zb and the 2D screen YB virtual. Mapping between spaces. Furthermore, the right side of the center line is exactly the same as FIG. Thus, we can see that two or more of the skewed space and 2D screen, a set can be defined and integrated in the display space to cover the wide angle of view.

      Now we describe the preferred method of drawing 2D screens in the first way, ie the texture mapping method. First, since the texture mapping method uses these principles and algorithms, we must describe a few geometric primitive drawing principles and algorithms. Geometric primitives include points, lines and triangular surfaces. These principles and algorithms can also be used to display volumetric 3D images of physical space colors.

      In general, the display space of a volumetric 3D display is composed of a 3D array of light elements. These light elements are shaped in different ways as described in the Background section. For convenience, these light elements are referred to as “lattice elements” (or generally “display elements”). Also for convenience, we use a system with a “rotary reciprocating” screen as an example to describe the principles and algorithms. This system is described in Tsao's Japanese Patent Application Notice 2002/268136 (FIG. 4b). It will be shown later that these principles and algorithms also apply to other types of volumetric 3D displays. Accordingly, the collection of grid elements in 3D space is like a 3D grid system as shown in FIG. A grid element is a 3D point having length, width and height as 201. The length 202 and width 203 correspond to the size of the projected image frame pixels. Height 204 is the “thickness” of one “frame” or “slice” of the volumetric 3D image, measured towards the screen motion. The length, width and height of each lattice element are dM, dN and dT, respectively. They are calculated with respect to the coordinate system used to render the data. For convenience, they are referred to as the “grid element scale”. For ease of description without loosening general relevance, the example assumes that the grid elements are aligned in a right angle manner.

      If the system projector uses a single DMD or FLCD with a white light source, each grid element is a binary (black or white) point. Instead, Tsao US Pat. No. 6,961,045 (also in Japanese Patent Application Notice 2003/1107399) (FIG. 6b-e) describes a method of “variable illumination”. “Variable illumination” illuminates each of a few adjacent pixels with different intensities. Each group of a small number of adjacent pixels is called a “composite pixel”. Composite pixels can display several gray scales. In such a case, each composite pixel can be defined as one grid element. Therefore, each grid element has a gray scale function.

      In a color volumetric 3D display based on three display panels or three sub-panels, there are three superimposed grid elements at each grid element position. There are three primary colors in three stacked grid elements. A collection of all grid elements of the same primary color is called a “field”. Thus, there are three superimposed fields in the display space of the color volume 3D display. Each field is like a monochromatic display except that it has a different primary color.

一般に、どの３Ｄ形でも３つの幾何基形の組合せによって表示することができる。各幾何基形は位置を定義する座標のデータを含んでいる。単色的なイメージでは、各幾何基形に「強度」データがある。「強度」データは幾何基形の輝度かグレイ・スケールを表す。色のイメージでは、各幾何基形に「色」データがある。一般に、「色」データは３つの原色の３つの強度の値を含んでいる。There are three basic geometric shapes:

In general, any 3D shape can be displayed by a combination of three geometric primitives. Each geometric primitive contains coordinate data defining a position. In a monochromatic image, each geometric base has “intensity” data. “Intensity” data represents the luminance or gray scale of the geometric basis. In a color image, each geometric base has “color” data. In general, the “color” data includes three intensity values for the three primary colors.

Render point geometry

      Point rendering is the mapping of point coordinates (x, y, z) to the position of one grid element of the 3D grid of FIG. FIG. 7 [A] faces the xz plane, as can be seen showing the lattice element structure. Each square grid represents a frame pixel, such as 301. The mapping is basically the position of one grid element (like 302) from one point (like P0). The mapping can also be from one point to more than one grid element. This is called “pixel dilation”. Pixel dilation adjusts the size of points to represent different brightness. Pixel dilation, indicated by P1, uses adjacent pixels to display different sizes of points. If 8 adjacent grid elements were used for expansion, and the point had a 3x3 grid element, it could have a level of 10 (0-9 grid elements, 0 representation black (or blank)). If 3 adjacent grid elements were used for expansion, then there are 2x2 grid elements (0-4 grid elements) with 5 size levels for 1 point.

      In general, the mapping of points is done in one “slice” (or “frame”). However, a mapping can also be created when desired for more than one slice. If the “thickness to slice” ds1 = dT (actual frame thickness) shown at 411 in FIG. 8B is used in the mapping, straight grid elements may be connected only at the corner 411. Good. As a result, the straight image can appear to be non-integral. By using a larger slice thickness, eg ds2 = 1.5 × dT, the point mapping can be made in two adjacent frames. Additional grid elements 412 are added to the straight line, making the straight line appear to be continuous. The same applies to the surface rendering example. The factor 1.5x is called “Over-Sampling Factor” (OSF).

Rendering a linear geometry

In general, point-based rendering is the preferred rendering method for lines and triangles. Point-based rendering includes two main steps:
(1) Changing the geometric base to a set of sample points representing the geometric base. Each sample point is a point geometry.
(2) Rendering of each sample point.

      In general, the luminance level of a geometric base is proportional to the number of displayed display elements. If the display element itself has a gray scale function, the brightness level is also proportional to the brightness scale of the display element. The total number of rendered display elements can be controlled to give the desired visual brightness by controlling the spatial distribution and size of the sample points.

ｎ＝０は点Ｐ０（ｘ０、ｙ０、ｚ０）であり、ｎ＝ＮｓはＰ１（ｘ１、ｙ１、ｚ１）である、全く２つの端ポイントを含むＮｓ＋１点がある。As illustrated in FIG. 8A, straight lines are sampled at equal intervals.
Assuming a straight line is divided into Ns sections, and sample points can be obtained as follows:

There are Ns + 1 points including exactly two end points, where n = 0 is the point P0 (x0, y0, z0) and n = Ns is P1 (x1, y1, z1).

      With point-based rendering, the density of point distributions and the size of each point along a straight line can be used to represent a straight line (or each field in a straight line) gray scale (or luminance or intensity). This is done for the optimal number of sample points (Ns_op + 1). (Ns_op + 1) is the minimum amount of sample points needed to fill all grid elements along a straight line when displayed on a volumetric 3D display. This gives the full intensity (brightness) of the straight line image. Ns greater than Ns_op does not add more lattice elements to the line and therefore does not further increase the brightness.

Ns_op for a linear geometry is calculated from the following scheme:

      Basically, Equation (102) calculates the minimum amount of sample points required in the x, y and z directions, respectively, and chooses the maximum number. The direction giving the maximum amount of sample points is called the “dominant sampling axis” or “dominant sampling direction”. The minimum spacing in each direction is directly related to the grid element scale. If pixel expansion is applied, the minimum spacing in the x and y directions is increased.

平行斜線の長方形は描画された格子要素を表す。直線のイメージはｚの方向で連続的である。支配的な見本抽出の軸線はｚ軸である。直線Ｌ２（ｘ−ｚの平面に平行直線）：
Ｎｓ＿ｏｐ＝ｉｎｔ［Ｍａｘ［０，６，４］＝６．
直線のイメージｚおよびｙの両方方向で連続的である。支配的な見本抽出の軸線はｙ軸である。FIG. 8B illustrates two simple examples that do not assume expanding pixels. Straight line L1 (vertical straight line):

A parallel diagonal rectangle represents a drawn grid element. The straight image is continuous in the z direction. The dominant sampling axis is the z-axis. Straight line L2 (straight line parallel to xz plane):
Ns_op = int [Max [0,6,4] = 6.
It is continuous in both directions of the straight line image z and y. The dominant sampling axis is the y-axis.

When Ns is less than Ns_op, a small amount of grid elements are drawn. Therefore, the brightness of the straight line is reduced. The “luminance ratio” of a linear geometric basis can be defined for the complete luminance of the line:
BR_1 ("Luminance ratio" of the linear geometric basis) = Br_1 / Br_1_op (103)
Br_1 = desired luminance level of the linear geometric base Br_1_op = full luminance level of the linear geometric base (ie, using the optimal number of sample points)

The luminance level of the geometric base is proportional to the number of drawn display elements. If the display element itself has a gray scale function, the brightness level is also proportional to the brightness scale of the display element. Therefore,
BR_1 = Nge_1 ^* Bge / (Nge_1_op ^* Bge_f) (104)
Nge_1 = number of grid elements to be drawn in a straight line Nge_1_op = number of grid elements in a straight line when completely drawn,
Bge = the brightness level of each rendered grid element Bge_f = the full brightness level of the grid element

When a line is completely drawn, the number of grid elements in the line can be expressed as follows according to the number of sample points:
Nge_1_op = Ns_op ^* Fd ² (106)
Ns_op is calculated from the equation (102).
Fd is a factor of pixel expansion in equation (102).
Similarly, the desired number of grid elements is:
Nge_1 = Ns ^* n_pd (107)
n_pd = “expansion number”
= Number of dilated pixels of the point (including the original one)
For example, if a 2 × 2 dilation (fd = 2) application, then n_pd takes a value between 0 and 4, indicating different levels of dilation.

Therefore, from equations (106) and (107), equation (104) is obtained:
^{BR_1 = (Ns / Ns_op) *} (n_pd / Fd 2) * (Bge / Bge_f) (108)
Ns ^* n_pd ^* (Bge / Bge_f) = Ns_op ^* Fd ^{2 *} BR_1 (109)
Equation (109) summarizes the rendering of a straight line with luminance ratio BR_1. It includes the effects of the number of sample points, pixel dilation and the gray scale capability of the grid elements. In general, a value (Ns, n_pd, (Bge / Bge_f)) of a set of satisfaction formulas (109) draws a straight line with a desirable luminance ratio BR_1.
If the pixel is binary and there is no dilation, then n_pd = (Bge / Bge_f) = fd = 1. Ns = Ns_op ^* BR_1 (110) represented by the formula (109)
Here, only linear brightness for point density control.
If Ns is fixed and (Bge / Bge_f), pixel expansion is the only control factor. For example, a 3x3 dilation gives a level of 10 brightness. A 4x4 expansion gives 17 levels.

Easy rendering of triangular geometry

      Simple rendering draws a triangular geometry by using only one layer of sample points. The preferred approach for obtaining sample points is “by straight line filling” the triangular surface. A straight line can then be drawn as a linear geometric basis. It controls the geometric base grayscale by controlling the density distribution and size of the sample spots.

      First, we describe how to completely draw a triangle. As in the case of straight line rendering, the basic approach to fully drawing a triangle is to draw just enough sample points so that the resulting grid element covers the triangle. The preferred steps are as follows:

(1) Calculate the optimal number of sample points for each of the three ends of the triangle using equation (102).
(2) Select the end with the most sample points as the “end of direction”, select the end with the least sample points as the “end of base”, and find the positions of the sample points at both ends. This gives the minimum amount of sample points to draw the triangle as completely as needed.

      (3) Draw a straight line from each sample point at the edge of the base of the mesh system on the triangle, draw a straight line from each sample point at the direction end, and draw a straight line from each sample point at the end of the direction; And assemble by making the straight line parallel to the edge of the base. The intersection of lines falling within the triangle indicates the position of the sample point to be drawn. See 圖 9.

      (4) Obtain all mesh and straight line sample points by using equation (101). Since the straight line is parallel to one of the two ends and the mesh size of the two ends is known, the number of sample points on each straight line can be easily calculated.

      (5) Rendering of all sample points. All straight lines parallel to the direction edge are drawn with the same density as the direction edge. All straight lines that are parallel to the edge of the base are drawn with the same density as the edges of the base. All the straight lines are drawn completely because both the direction edge and the base edge are completely drawn. Therefore, the point density is optimal in all directions. See FIG. By constructing the rendering mesh based on the two ends of the triangle and setting the optimal mesh size independently in two directions, the above algorithm gives roughly uniform point densities for triangles of different sizes.

In order to display a more completely luminance triangle, the total number of sample points is reduced to match the reduced luminance. The luminance ratio is:
BR_st (luminance ratio of triangular surface) = Br_st / Br_st_op (201)
Br_st = desired luminance level of the triangular plane Br_st_op = full luminance level of the triangular plane (ie, using the optimal number of sample points)

The luminance level of the geometric base is proportional to the number of drawn display elements. If the display element itself has a gray scale function, the brightness level is also proportional to the brightness scale of the display element. Therefore,
BR_st = Nge_st ^* Bge / (Nge_st_op ^* Bge_f) (202)
Nge_st = number of grid elements to be drawn on the triangular plane Nge_st_op = number of grid elements on the triangular plane when completely drawn,

式（２１０）は輝度比率ＢＲ＿ｓｔの三角面のレンダリングを要約する。それはサンプル点の数、ピクセルの膨張および格子要素のグレースケールの機能の効果を含んでいる。一般に、一組の満足式（２１０）の値は望ましい輝度比率ＢＲ＿ｓｔで三角面を描画する。When a triangle is completely drawn, the number of triangular grid elements can be expressed by the number of sample points as follows:
Nge_st_op = (the number of sample points on the triangular surface to be completely drawn) ^* Fd ² (203)
Fd is a factor of pixel expansion in equation (102).
(Number of sample points on the triangular surface to be completely drawn) = Ns_op_b ^* Ns_op_d / 2 (204)
Ns_op_b = optimum number of sample points at the edge of the base Ns_op_d = optimum number of sample points at the edge of the direction
^{Nge_st_op = Ns_op_b * Ns_op_d * Fd 2} /2 (205)
Nge_st (desired number of lattice elements) = Ns_b ^* Ns_d ^* n_pd / 2 (206)
Ns_b = number of sample points at the edge of the base Ns_d = number of sample points at the edge of the direction

Equation (210) summarizes the rendering of the triangular plane of the luminance ratio BR_st. It includes the effects of the number of sample points, pixel dilation and the gray scale capability of the grid elements. In general, the value of the set of satisfaction formulas (210) draws a triangular plane with a desirable luminance ratio BR_st.

Ns_b and Ns_d are calculated by the following equation similar to equation (102):
Ns = int [Max [Δx / dx, Δy / dy, Δz / dz]] (102A)
Δx is the span in the x direction at the end, interval for calculating dx = Ns Δy is the span in the y direction at the end, interval for calculating dy = Ns Δz is the span in the z direction at the end , Dz = Ns In general, dx is different from dM and dN, and since pixel expansion operates mainly in the dM_dN direction, dx, dy, dz are triangular planes relative to the lattice element structure. Calculated according to orientation. This affects the selection of the optimal sampling interval for the edge. There are three cases:

ｓｑｒｔ［内容］：内容の二乗根操作
ｄｚは式（２１４）から得ることができるおよびＮｓは得ることができる。Case (1): The dominant sampling direction at both the base end and the direction end is the z-axis. From equation (102A):
Ns = int [Δz / dz]
From equation (102):
Ns_op∝Δz / dz_op
Ns / Ns_op = dz_op / dz = dT / dz (212)
From equations (210) and (212):

sqrt [content]: The square root operation dz of the content can be obtained from equation (214) and Ns can be obtained.

一般に、ｄＭ＝ｄＮはおよび私達ｄｘ＝ｄｙを取ることができる。式（２１０）および（２１６）から：

Case (2): The dominant sampling direction at both the base end and the direction end is the x or y axis. From equation (102A):
Ns = int [Δx / dx] or int [Δy / dy]
From equation (102):

In general, dM = dN and we can take dx = dy. From equations (210) and (216):

ｄｘ＜ｄＴが、それからｄｚ＝ｄＴを取れば。（２２０）から：
ｄｘ／（ｎ＿ｐｄ^＊Ｂｇｅ／Ｂｇｅ＿ｆ）＝ｄＭ／（Ｆｄ^＊ＢＲ＿ｓｔ） （２２２）
従って、

すなわち、式（２２４）の状態の下で、ｄｚ＝ｄＴおよび式（２２２）から計算したｄｘを式（１０２Ａ）で使用する。
ｄｘ＞＝ｄＴが、それからｄｚ＝ｄｘを取れば。（２２０）から：

すなわち、式（２２８）の状態の下で、式（２２６）から計算したｄｘを式（１０２Ａ）で使用する。Case (3): One of the two ends has the sample direction dominant on the z axis and the other on the x or y axis. The following procedure is preferred. The procedure gives an approximately equally spaced mesh in two directions,
Coupling of formulas (210), (212) and (216):

If dx <dT, then take dz = dT. From (220):
dx / (n_pd ^* Bge / Bge_f) = dM / (Fd ^* BR_st) (222)
Therefore,

That is, dx = dT and dx calculated from equation (222) are used in equation (102A) under the condition of equation (224).
If dx> = dT, then take dz = dx. From (220):

That is, dx calculated from the equation (226) is used in the equation (102A) under the state of the equation (228).

Multilayer rendering of triangular geometry

      When simple rendering is applied, the total number of grid elements in a specified triangle is fixed. This number limits the number of levels of brightness that can actually be displayed and sensed. More triangular grid elements can display more brightness levels. Multi-layer rendering uses one or more triangular surfaces (called auxiliary surfaces) in a single triangular rendering. FIG. 10A illustrates the idea. The principle is to stack a plurality of auxiliary surfaces 1101a — 1101c closely together. Visually they are like a triangle. Practically more grid elements are used to represent more levels of brightness. And there is minimal distortion to the original shape.

A hypothetical NL auxiliary surface is used and the desired luminance ratio is BR_ms, described after the rendering procedure. The concept of luminance ratio and equations (201) and (202) still apply. However, for clarity, equation (201) is rewritten as for the case of multiple auxiliary surfaces,
BR_ms (luminance ratio) = Br_ms / Br_ms_op (301)
Br_ms = desired luminance level of the triangular surface Br_ms_op = complete luminance level of the triangular surface Br_ms_op = NL ^* Nge_ss_op ^* Bge_f
Nge_ss_op = number of grid elements of one full brightness auxiliary surface
BR_ms = Nge_ms ^* Bge / (NL ^* Nge_ss_op ^* Bge_f) (302)
Nge_ms = number of grid elements to be drawn in a triangular plane = total number of grid elements on all NL auxiliary surfaces.
From equation (302) we see that the sum of the luminance ratios of the auxiliary surfaces is equal to the luminance ratio of the triangular surface,
BR_ms = BR_ss_0 + BR_ss_1 +. . . + BR_ss_ (NL-1) (304)

各補助表面は描画されるべき元の三角面と同じサイズ、形およびオリエンテーションの１つの三角面である。各々の補助表面のＢＲ＿ｓｓの輝度比率はまたＢＲ＿ｓｔと同じ方法定義される。そう、補助表面は三角面の簡単なレンダリングとによって同じ方法丁度描画することができる。In general, similar results give a combination of auxiliary surface luminance ratios that satisfy equation (304).
But the following is the most convenient method:

Each auxiliary surface is one triangular surface of the same size, shape and orientation as the original triangular surface to be drawn. The brightness ratio of BR_ss for each auxiliary surface is also defined in the same way as BR_st. So, the auxiliary surface can be drawn exactly the same way with a simple rendering of a triangular surface.

The spacing (ts) between two adjacent auxiliary surfaces has a preferred minimum value that prevents overlapping grid elements of the same frame, as illustrated in FIG. 10B.
ts = ds ^* sin α
ds = dT ^* OSF
α is the angle between the surface normal and the horizon.
Unit normal vector N = [nx, ny, nz] triangular plane,
ts = ds ^* | nz | (505)
When α becomes smaller, Ts becomes smaller. If Ts is smaller than dM ^* Fd according to equation (505), then the following minimum value should be used:
ts = dM · Fd (505A)
The auxiliary surface can be found by calculating the highest point of the corner along the direction of the normal of the triangle:
(X, y, z) j, k = (xj−k ^* ts ^* nx, yj−k ^* ts ^* ny, zj−k ^* ts ^* nz) (507)
(Xj, yj, zj) is the highest point of the original triangle face j = 0, 1, 2 (the highest point of the three corners)
k = 0, 1,. . . NL-1 is the index of the auxiliary surface.

      As shown in FIG. 11A, a 2D coordinate system (u, v) that covers the entire 2D bitmap is defined. The range of coordinates (u, v) is between (0,0) and (1,1). There are M pixels in the u direction and N pixels in the v direction in the bitmap. Each pixel is represented by an integer index [M, N] where M = 0, 1, 2,. . . M-1 and N = 0,1,2. . . N-1 can be found. Therefore, there is a mapping between [m, n] exponent and (u, v) coordinates.

      The mapping of the bitmap texture to the triangular plane is defined by the corresponding 2D triangle in the uv plane. The corresponding triangle corresponds to the 3D triangular face (called UVT for clarity) by the highest point of the three corners (called 3DT for clarity). The mapping between the bitmap area covered by UVT and 3DT is based on a linear ratio. Accordingly, as described in FIG. 11B, a mapping between a 3DT group 1211 and a UVT group 1210 covering the desired bitmap area can also be made.

Color texture mapping and rendering is done one field at a time. That is, the color bitmap is initially divided into three field maps (R (red) field, G (green) field, and B (blue) field). Each field map is therefore a monochromatic image map and can be drawn by the same procedure. The optics of the volumetric 3D display then recombine the three fields and show a map of color texture. The basic procedure for drawing a triangular surface of a monochromatic texture map is as follows:
(1) Divide the full intensity scale of the texture map into a number of different intensity ranges. Thus, each intensity range corresponds to a different region of the texture map.
(2) Establish a mapping from each region of the texture map to the corresponding region of the triangle. Use the UVT-3DT mapping procedure described previously.
(3) Assign a brightness level to each corresponding area of the triangle based on the intensity range of the area according to the mapping. The luminance ratio is defined in the same way as previously described.
(4) Draw each corresponding area of the triangle of different density of display elements to represent different brightness levels. Point-based rendering is the preferred method. Basically, each corresponding area of the surface is drawn under a mesh system that gives the desired brightness to the entire surface, but the sample points are placed only within the corresponding area.

The detailed steps are as follows:
Step 1: Get the red, green and blue intensity values for each pixel from the bitmap and set up three pixel data structures:
Pixel_Rfield [m] [n]. intensity = FI (field intensity) R;
Pixel_Gfield [m] [n]. intensity = FIG;
Pixel_Bfield [m] [n]. intensity = FIB;
FI stands for field intensity.
Step 2: In each field, divide the strength scale, 1250, into the Nrgn region. The part must not be between intensity 0 and FI_full. If desired, the split can be placed between FI_low and FI_high, see FIG. 11C.

Step 3: In each field, assign each pixel to one of the Nrgn “regions” according to the intensity value FI. Regional index for region i:
i = (int) [((FI-FI_low) / (FI_high-FI_low)) ^* Nrgn]
(Int) [content]: Set up the data structure of the lowest integer manipulated region index less than the acquired “content” (using the R (red) field as an example)
Pixel_Rfield [m] [n]. region_idx = i; (700A)

これは三角面のこの地域を描画するのに使用されるべき輝度比率ＢＲである。
ＢＲが計算されれば、私達はそれから三角面のこの地域を描画するために前に記述されている簡単レンダリングか多層レンダリングを使用してもいい。多層レンダリングが使用されれば、補助表面それぞれの輝度比率は更に式（３０３）によって計算されるべきである。Step 4: Draw the area of triangle 1 at a time. In region i, take the lower intensity of this region to find the corresponding luminance ratio BR [i]. Use linear interpolation according to Figure 11 [C]:

This is the luminance ratio BR that should be used to draw this region of the triangle.
Once the BR is calculated, we can then use the simple rendering or multi-layer rendering described previously to render this region of the triangle. If multi-layer rendering is used, the luminance ratio of each auxiliary surface should be further calculated by equation (303).

The rendering of a known luminance ratio region i includes the following steps:
(Step 4.1): Determine the number of sample points ((Ns_b [i] +1) and (Ns_d [i] +1)) at the edge of the base of the 3D triangle (3DT) and the edge in the direction. Use simple rendering or multilayer rendering and follow the corresponding procedure.

      (Step 4.2): Apply Ns_b [i] and Ns_d [i] to the corresponding UVT of the triangle and calculate the sample points (u, v) j, k. The calculation of the sample points is the same as before, with each grid line using equation (101) with the exception that (u, v) replace (x, y) and the Z coordinate is zero. See FIG. 11 [D].

３ＤＴの基盤の端は（ｘａ，ｙａ，ｚａ）から（ｘｂ，ｙｂ，ｚｂ）にあり、方向の端は（ｘｂ，ｙｂ，ｚｂ）から（ｘｃ，ｙｃ，ｚｃ）にある。(Step 4.3): Check each calculated sample point (u, v) j, k to see if it belongs to this current area i, only the points belonging to area i are drawn with this current point density The That is, check the index [m] [n] of the corresponding pixel array at the discovery (u, v) point, then check the data structure to see if the following is true:
Pixel_Rfield [m] [n]. region_idx = i;
If that is not true, calculate the next (u, v) sample point.
Calculate the corresponding point (x, y, z) j, k of this (u, v) j, k and draw it in 3DT. This is simply using this exponent (j, k) and adding equation (101) to 3DT.

The end of the 3DT base is from (xa, ya, za) to (xb, yb, zb), and the end of the direction is from (xb, yb, zb) to (xc, yc, zc).

      In this way, texture bitmaps can be drawn on the surface of a triangular surface, one region at a time. FIG. 11E illustrates three regional triangles with different luminance (intensity). Therefore, there are three mesh systems in the triangle. It is used to check whether the regional index data structure is within the region to be sampled efficiently.

      Accordingly, rendering of a perspective view of a 2D screen can be performed by applying the texture mapping method described above.

Supplementary description

      Another preferred method of rendering is cross-based rendering. A simple cross-based rendering renders a geometric base by calculating the intersection with the slice frame and controlling the pixel density of the cross-frame bitmap of the slice frame.

      In general, each intersection is a small bitmap that contains the pixels of the frame. Stitching all small bitmaps of intersection together forms a conceptual “composite bitmap”. The desired brightness level is then expressed by controlling the ratio of the number of pixels rendered relative to the total number of pixels in the composite bitmap. The small bitmap is then redrawn by the inverse mapping from the composite bitmap being drawn. The redrawn small bitmap then forms a geometric base at the desired brightness level.

      For straight line rendering, the composite bitmap is organized as a 1D bit string. In the rendering of the triangular surface 1001, each intersection with a frame slice 1002 is a small bitmap 1003 of the frame pixel configuration, as illustrated in FIG. Stitching all the small bitmaps of the intersection together forms a 2D composite bitmap 1004.

The concept of luminance ratio and equations (201) and (202) still apply. And the fully drawn triangle is still used as a reference. The number Nge_st of triangular lattice elements is basically the number Np_CBM_st of pixels in the composite bitmap.
Nge_st = Np_CBM_st = Number of drawn pixels of the composite bitmap Nge_st_op = Np_CBM_st_f (completely drawn)

For convenience, the composite bitmap is represented in the uv plane as shown in FIG. Rendering takes place in two directions: the u- and v-directions.
To draw at full brightness (fully full), the spacing between the drawn pixels in two directions is set to the pitch of the projected pixels:
du_op = dv_op = dL_p_op = dM = dN.

Np_CBM_st is inversely proportional to the square of dL_p of the rendering interval:
Np_CBM_st∝ (1 / dL_p) ²
Therefore,
Nge_st / Nge_st_op = Np_CBM_st / Np_CBM_st_f = (dL_p_op / dL_P) ² (240)
From Expression (240), Expression (202) is satisfied. BR_st = (dL_p_op / dL_p) ^{2 *} (Bge / Bge_f) (242)
From dL_p_op = dM = dN,
dL_p / sqrt (Bge / Bge_f) = dM / sqrt (BR_st) (244)

Equation (244) provides the desired spacing between adjacent drawn pixels in a triangular composite bitmap that gives the desired luminance ratio BR_st. If the pixel has no grayscale capability (Bge / Bge_f = 1), (dL_p) ² is inversely proportional to BR_st. Once dL_p is obtained, the next two steps complete the rendering:
(1) The composite bitmap is redrawn according to the new interval dL_p. Remove pixels that do not match the new distance.
(2) The current desired luminance ratio to these modified intersection small bitmaps, which removes the corresponding pixels removed in step (1) from the original, fully filled intersection small bitmaps There is BR_st.

      In general, the rendering method described in this invention can be applied to volumetric 3D displays with any form of display element distribution. The frame slice direction and dM, dN and dT can be defined.

      For example, if the volumetric 3D display is based on a rotating display panel (or screen), then there is no dT fixed value. In this case, the key is to get a sufficiently small dT just so that the rendering method works and the computation is time-minimized. dT also depends on the position of the geometric primitive in the display space.

ＣｏｓαおよびＯｍＰｍは得ることができる：

FIGS. 13A and 13B illustrate an example of a rotating display system. In general,
dT = rdθ,
dθ is the lowest corner space between two adjacent frames, eg 1581 and 1582, and r depends on the position of the point being drawn.
Rendering of the straight line P1P2,
dT = OmPmdθ,
OmPm is the shortest distance between the straight line and the rotation axis 1501. OmPm can be calculated from a straight line projection in the X_Y plane.

Cosα and OmPm can be obtained:

If Pm is outside the straight line, apply the following formula to each corner point Pi (xi, yi, zi) as illustrated in FIG. 13 [C] [D]:
dTi = rdθ = sqrt (xi ² + yi ² ) dθ
The lowest dTi should be used as dT.

      In the rendering of a triangular plane, we do a calculation to find the above minimum dT at the three ends of the triangle.

To determine ts for multi-layer rendering, the states are similar. As illustrated in FIG. 14, the vector N is a triangular unit normal vector, and Nxy is an XY plane projection.
ts_xy = dT ^* sinβ
dT = rdθ = sqrt (x2 ² + y2 ² ) dθ
ts = ts xv ^* cos α
Sinβ and Cosα can all be calculated from the vector N. Apply the above procedure to the three corner points and find the largest Ts.

      In point-based rendering, the number of sample points at the two ends of the triangle is matched to the control point density. Different mesh sizes represent different luminance ratios. Alternatively, we can use a fixed mesh size. Different numbers of points can represent different luminance ratios under the same mesh size. The same applies to cross-based rendering. A fixed pixel mesh size may be more suitable for a composite bitmap because the bitmap has an inherent mesh size (ie, a pixel grid).

      Algorithms and data structures are described describing the software in the form of. However, they can also be executed especially when executed in electronic systems where the algorithm is embedded in firmware or digital electronic circuitry.

Supplementary description 2: Voxel mapping method

      Based on the similar spirit of the previously described rendering method, we describe the principles and algorithms of 3D volume rendering in distributed gray scale (or similar properties) in this section. The basic procedure is similar to surface rendering with texture maps, with the exception that the mesh system and sampling were done in three dimensions. Gray scale is represented by controlling the distribution of size and density of dispersed spots. This allows the display of a 3D volume color or gray scale distribution by a volumetric 3D display based on binary pixels without sacrificing resolution. This is useful for applications such as medical or mining visualization.

Usually, the 3D volume (1360) to be done is a set of orthogonally structured volume 3D data. Shown in FIG. 15A, it basically gets the C bitmaps stacked together. Each layer of the stack is an AxB bitmap. A, B and C are integers. Therefore, the total number of voxels is AxBxC. Each data voxel can be found by three integer exponents (a, b, c):
a-lateral direction of the data layer; from pixel index (0, b) to (A-1, b);
b-vertical direction of the data layer; from pixel index (a, 0) to (a, B-1);
c-stacking direction; layer index # 0 to # C1

As shown in FIG. 15B, a 3D box 1380 is defined to closely surround the 3D volume.
Four corner points are defined:
P0 (x0, y0, Z0)-corner point P1 (x1, y1, z1) at the corresponding voxel (0, 0, 0)-corner point P2 (at the corresponding voxel (A-1, 0, 0) x2, y2, z2) -corresponding voxel (0, B-1,0) at the corner point P3 (x3, y3, z3) -corresponding voxel (0,0, C-1) at the four corner points By placing the coordinates of the corner points, the position and orientation of the 3D volume with respect to the xyz coordinate system can be determined. The four corner points form three right-angle “corner vectors”: vector P0P1, vector P0P2, vector P0P3.

      This algorithm is similar to the region based approach of 3DT rendering with texture maps. However, the algorithm is applied in 3D (3 directions in space) and extra 3D volume boxes. Each rendering is performed in each color field. That is, the 3D volume is primarily divided into three fields (R field, G field, and B field). Each field can therefore be drawn with a monochromatic volume and the same procedure. The optics of the volumetric 3D display then recombine the three fields. In single field 3D volume rendering, the 3D volume is primarily divided into several regions. Each region has a different intensity (luminance) range. From the intensity range of each region, the corresponding luminance ratio for that region can be defined. For each region of known luminance ratio, the amount of three perpendicular sample points can be calculated. Once the number of sample points in each direction is obtained, the “mesh size” (or grid size) for that region can be determined. Therefore, the 3D box is drawn in one area at a time from the corresponding luminance ratio. Basically, each region of the 3D volume is drawn under a mesh system that gives the desired luminance ratio to the entire 3D box, but sample points are placed only in the corresponding region.

The basis of the Voxel mapping method is the rendering of a 3D box with a certain luminance ratio. Luminance ratio of 3D box:
BR_box = Br_box / Br_bx_op (801)
Br_box = desired brightness level of 3D box to be rendered Br_box_op = luminance level of 3D box when fully rendered (optimum number of sample points)

The brightness level of the 3D box is proportional to the number of drawn grid elements. It is also proportional to the brightness scale of the grid element itself if the grid element has a gray scale function.
Therefore,
BR_box = Nge_box ^* Bge / (Nge_box_op ^* Bge_f) (802)
Nge_box = number of grid elements to be drawn in the 3D box Nge_box_op = number of grid elements in the 3D box when completely drawn,
Bge = the level of brightness of the grid element when each drawing is made Bge_f = the level of full brightness of the grid element

The number of grid elements in a fully rendered 3D box can be related to the number of sample points as follows:
Nge_box_op = (number of fully drawn 3D box sample points) ^* Fd ² (803)
Fd is a factor of pixel expansion in equation (102).
Number of fully drawn 3D box sample points = Ns_op_a ^* Ns_op_b ^* Ns_op_c (804)
Ns_op_a = optimal amount of sample point at end P0P1 Ns_op_b = optimal amount of sample point at end P0P2 Ns_op_c = optimal amount of sample point at end P0P3
Nge_box_op = Ns_op_a ^* Ns_op_b ^* Ns_op_c ^* Fd ² (805)
In general,
Nge_box = Ns_a ^* Ns_b ^* Ns_c ^* n_pd (806)
Ns_a = amount of sample points at end P0P1 Ns_b = amount of sample points at end P0P2 Ns_c = amount of sample points at end P0P3 n_pd = “expansion number”
= Number of dilated pixels of the point (including the original one)
Therefore,

      Ns_a, Ns_b, and Ns_c are calculated by the equation (102A). Since dT is different from dM and dN, and pixel expansion operates mainly in the dM-dN direction, dx, dy, dz are calculated according to the orientation of the 3D box relative to the grid element structure. This affects the selection of the optimal sampling interval for the edge. There are four cases:

ｄｚは式（８１４）から得ることができるおよびＮｓは得ることができる。Case (1): The dominant sampling direction of all three right-angle ends is the z-axis. From equation (102A):
Ns = int [Δz / dz]
From equation (102):
Ns_op∝Δz / dz_op
Ns / Ns_op = dz / op / dz = dT / dz (812)
From equations (810) and (812):

dz can be obtained from equation (814) and Ns can be obtained.

一般に、ｄＭ＝ｄＮはおよび私達ｄｘ＝ｄｙを取ることができる。式（８１０）および（８１６）から：

Case (2): The dominant sampling direction of all three right-angle ends is the x or y axis. From equation (102A):
Ns = int [Δx / dx] or int [Δy / dy]
From equation (102):

In general, dM = dN and we can take dx = dy. From equations (810) and (816):

ｄｘ＜ｄＴが、それからｄｚ＝ｄＴを取れば。（８２０）から：
（ｄｘ）^２／（ｎ＿ｐｄ^＊Ｂｇｅ／Ｂｇｅ＿ｆ）＝ｄＭ／ＢＲ＿ｂｏｘ （８２２）
従って、

すなわち、式（８２４）の状態の下で、ｄｚ＝ｄＴおよび式（８２２）から計算したｄｘを式（１０２Ａ）で使用する。
ｄｘ＞＝ｄＴが、それからｄｚ＝ｄｘを取れば。（８２０）から：
（ｄｘ）^３／（ｎ＿ｐｄ^＊Ｂｇｅ／Ｂｇｅ＿ｆ）＝ｄＭ^＊ｄＴ／ＢＲ＿ｂｏｘ （８２６）
ＢＲ ｂｏｘ＜＝（ｎ ｐｄ^＊Ｂｇｅ／Ｂｇｅ＿ｆ）^＊ｄＭ／（ｄＴ）^２ （８２８）
すなわち、式（８２８）の状態の下で、式（８２６）から計算したｄｘを式（１０２Ａ）で使用する。Case (3): One of the three ends has the sampling direction dominant on the z axis and the other on the x or y axis. This should be the usual case.
Coupling of formulas (810), (812) and (816):

If dx <dT, then take dz = dT. From (820):
(Dx) ² / (n_pd ^* Bge / Bge_f) = dM / BR_box (822)
Therefore,

That is, dx = dT and dx calculated from equation (822) are used in equation (102A) under the condition of equation (824).
If dx> = dT, then take dz = dx. From (820):
(Dx) ³ / (n_pd ^* Bge / Bge_f) = dM ^* dT / BR_box (826)
BR box <= (n pd ^* Bge / Bge_f) ^* dM / (dT) ² (828)
That is, dx calculated from the equation (826) is used in the equation (102A) under the state of the equation (828).

ｄｘ＜ｄＴが、それからｄｚ＝ｄＴを取れば。（８３０）から：
ｄｘ／（ｎ＿ｐｄ^＊Ｂｇｅ／Ｂｇｅ＿ｆ）＝ｄＭ／（Ｆｄ^＊ＢＲ＿ｂｏｘ） （８３２）
従って、

すなわち、式（８３４）の状態の下で、ｄｚ＝ｄＴおよび式（８３２）から計算したｄｘを式（１０２Ａ）で使用する。
ｄｘ＞＝ｄＴが、それからｄｚ＝ｄｘを取れば。（８３０）から：

すなわち、式（８３８）の状態の下で、式（８３６）から計算したｄｘを式（１０２Ａ）で使用する。Case (4): One of the three ends has the sampling direction dominant on the x or y axis and the other on the z axis. Coupling of formulas (810), (812) and (816):

If dx <dT, then take dz = dT. From (830):
dx / (n_pd ^* Bge / Bge_f) = dM / (Fd ^* BR_box) (832)
Therefore,

That is, under the state of Expression (834), dz = dT and dx calculated from Expression (832) are used in Expression (102A).
If dx> = dT, then take dz = dx. From (830):

That is, dx calculated from the equation (836) is used in the equation (102A) under the state of the equation (838).

      We now describe the mapping between 3D volume voxel (exponential (a, b, c)) and 3D box mesh points (exponential (i, j, k)). The voxel index (a, b, c) is from (0, 0, 0) to (A-1, B-1, C-1) as described previously. The mesh point index (i, j, k) is from (0, 0, 0) to (Ns_a, Ns_b, Ns_c) based on the index definition used in equation (101). We use direction “a” as an example. The same principle applies "b" and "c" in the other two directions.

Case (A): Mesh point interval (dLa)> voxel pitch (dA), that is, Ns_a <A. FIG. 16A illustrates the state. Reference numeral 1401 denotes a mesh lattice. It represents the point position of the mesh point (ie, the intersection) of the index “i” mesh line. Reference numeral 1402 denotes a voxel lattice. Since the voxel has size, it represents the exponent “a” partition, in which case it is more efficient to calculate the sample points from the (i, j, k) space. The mapping is to see which section “a (i)” corresponds to the point “i”. Mapping can be done in the space of a ratio index without the need for xyz dimensions.
(I-0) / (Ns_a-0) = (a (i) -0) / A
Therefore,

      Case (B): Mesh point interval (dLa) <= voxcl pitch (dA), that is, Ns_a> = A. FIG. 16B illustrates the state. In this case, it is more efficient to calculate the sample points from the (a, b, c) space. In each region, we process only voxels with the correct intensity. Mapping is to cover and point which point “a” covers. Mapping can be performed again in the space of the ratio index without the need for xyz dimensions.

The left (small) end 1403 of section “a” corresponds to position “ia” in i-space. The section has a length of L_a (1404).

Now we describe the detailed steps:
Step 1: From the 3D volume, get R, G, B intensity values for each voxel and set up three voxel data structures:
Voxel_Rfield [a] [b] [c]. intensity = FI (field intensity) R;
Voxel_Gfield [a] [b] [c]. intensity = FIG;
Voxel_Bfield [a] [b] [c]. intensity = FIB;
Step 2: In each field, divide the intensity scale into Nrgn “regions”. The part must not be between intensity 0 and FI_full. If desired, the part can be placed between FI_low and FI_high. As shown in FIG. 11C, the highest Nrgn is one area of FI_full, that is, one gray level.

Step 3: In each field, assign each voxel to one of the Nrgn “regions” according to the strength level FI of voxcl:
Region r, (r = 0, 1, 2,... Nrgn-1):
r = (int) [((FI_FI_low) / (FI_high_FI_low)) ^* Nrgn]
Set up regional index data structure (using R field as an example)
Voxel_Rfield [a] [b] [c]. region_idx = r;
In addition, set up the data structure of the group of voxels and collect the indices of voxels belonging to the same region (same range of intensity). That is, the data structure Voxel_Group [r] includes all voxels (a, b, c) belonging to the same region r.

これは３Ｄ箱のこの地域ｒを描画するのに使用されるべき輝度比率ＢＲである。Step 4: Draw a 3D box, one region at a time. The lower strength of region r is as follows:
FI = r ^* (FI_high−FI_low) / Nrgn
BR [r] for the corresponding luminance ratio

This is the luminance ratio BR to be used to draw this region r of the 3D box.

The detailed steps for the rendering of the region “r” of the known luminance ratio BR [r] of the single field 3D volume box are as follows:
(Step 4.1) Obtain the number of respective sample points at the three right ends: Ns_a, Ns_b and Ns_c according to the method described previously.
(Step 4.2) Inspection:
If Ns_a <A, Ns_b <B, and Ns_c <C, the sample points should be calculated from the (i, j, k) space for efficiency (case (A) described earlier). Go (step 4.3).
Otherwise, the sample points should be calculated from the (a, b, c) space. Go (step 4.4).

(Step 4.3) Sample points for calculation from (i, j, k) space to (a, b, c) space.
First, obtain the corresponding voxcl position (a, b, c) of each mesh point (i, j, k) by using equation (710). Then use the data structure established in step 1 to check each corresponding voxel for belonging to this region r. Only points corresponding to voxels in this region “r” should be drawn. Sample points (x, y, z) _{i, j, k} can be calculated by the following formula:

(Step 4.4) Sample points for calculation from (a, b, c) space to (i, j, k) space.
First find each voxel in this region “r” from the predefined data structure voxel_Group [r]. For each of those voxels, find the index (ia, jb, kc) of the points covered by this voxel by using equation (711). Draw these points corresponding to each voxel in this region by using the equation (600) and the indices (x, y, z) ia, jb, kc.

      In FIG. 11C and formula (702), the range of the luminance ratio (BR) is expressed in the generalized form of the uppermost BR_high and the lowermost BR_low. The highest luminance ratio, BR_op, is naturally 1. Usually, the mapping may be a linear mapping. That is, FI = 0 corresponds to BR = 0, and FI = FI_full corresponds to BR = 1. By choosing a low-high window on both the FI and BR axes for mapping, we can handle the brightness level of the displayed image. This can enhance or suppress a certain range of data. Furthermore, the mapping need not be linear. The mapping line 1251 may be a curve.

      One application of BR low-high window processing is to enhance local information in D volume images. One practical problem with displaying 3D volume data, such as CT or MRI medical imaging data on volumetric 3D displays, is that the foreground and background images of the local area of interest can interfere with viewing. This is because the volume 3D display image is essentially transparent. One solution is to add a “scan box” to see the local area of interest. The image inside the scan box is displayed at a normal or increased brightness ratio. The image outside the scan box is displayed with a reduced overall luminance ratio. FIG. 17 illustrates the idea. Reference numeral 1801 denotes a 3D data volume displayed as a volume 3D image. Small box 1802 is defined as a scan box. The portion of the image in the scan box is displayed with a normal BR window, eg BR_high = 1 and BR_low = 0. The portion of the image outside the scan box is displayed with a suppressed BR window, eg BR_high = 0.3 and BR_low = 0.

      Indeed, the 3D volume is first partitioned into two 3D volumes, a large volume corresponding to the original 3D box and a small volume corresponding to the new scan box. The two volumes are then drawn separately by the Voxel mapping procedure using different BR windows. The scan box is drawn after the original 3D box. It can therefore be overwritten in a large volume. This can be used to aid exploration for geological features of harmful tissue or mine seismic data in 3D medical imaging data.

      An example of a skewed coordinate system of the basic concept of the present invention will be shown.       2 shows a geometric analysis of the first example coordinate system mapping of the present invention.       A refining image frame is placed near the bottom of the rotary reciprocating display.       2 Implement the projector.       2 shows a geometric analysis of the mapping of the coordinate system of the second example of the present invention.       1 shows a system of display elements of a typical volumetric 3D display.       Shows how to render a point.       Demonstrates a straight point-based rendering method.       Shows the method of point-based rendering of a triangular surface.       A method of multi-layer rendering of a triangular surface is shown.       The method of surface texture mapping is shown.       3 illustrates a rendering method based on the intersection of triangular faces according to the present invention.       Fig. 4 shows the calculation of dT for a rotating display system.       The ts calculation of the rotating display system will be described.       2 illustrates a Voxel mapping method of the present invention.       The mapping between voxels and sample points is shown.       2 illustrates a scan box method of the present invention.

Explanation of symbols

15 Projector 201 Grating element 450 Point position 451 in undistorted coordinate system Point position 550 in skewed coordinate system according to mapping Additional refined frame 570 Moving screen track 580a-d Between two adjacent frames Rotation angle 590a-f Frame position 601 Another 2D projector 602 Switchable reflector 1001 Triangular plane 1002 Slice of frame 1003 Small bitmap 1004 Composite bitmap 1101a-c Auxiliary surface 1210 Corresponding triangle (UVT) on bitmap
1211 3D triangular surface (3DT)
Dividing the bitmap one field intensity scale into regions of 1250 Nrgn 1251 Mapping curve from one field intensity scale of bitmap to luminance ratio

Claims (30)

A method for displaying 3D data defined in a continuous space of a volumetric 3D display comprising:
(1) defining a finite space of a volumetric 3D display with a skewed coordinate system and a 2D screen;
(2) establishing a coordinate system mapping between a first portion of the continuous space and a skewed coordinate system of the finite space;
(3) The remaining parts of the continuous space and the virtual part in the 2D screen. Establishing a coordinate system mapping between spaces;
(4) According to the mapping of the coordinate system, the portion of the 3D data that is within the first portion of the continuous space is displayed in the finite space, and within the remaining parts of the continuous space Displaying the portion of the 3D data that is present on the 2D screen in a perspective view;
Including said method. The mapping of the coordinate system is
(1) the step of selecting the eye position,
(2) defining a reference plane in the continuous space and determining a reference position of the reference plane, the step appearing when the reference plane is viewed from the eye position having the same size as the 2D screen Step,
3. The method of claim 1 including defining a first portion of the continuous space such that a portion of the continuous space within the reference plane.       The method of claim 1, wherein the step of displaying a perspective view of the 2D screen includes rendering the 2D screen using the bitmap by rendering the perspective and texture mapping as a bitmap.       The method of claim 1, wherein the volumetric 3D display includes a moving display surface that displays and distributes an image frame and forms a volumetric 3D image, the 2D screen being mounted nearby and parallel to one of the image frames. .       Generating an additional image frame on the display surface, wherein the moving display surface is a rotary reciprocating surface and is near the top or bottom position of the 2D screen or display surface rotation, forming the 2D screen; 5. The method of claim 4, further comprising:       6. The display period of the additional image frame has a predetermined ratio, and the additional image frame represents a gray scale or a color level of the 2D screen according to a principle of pulse-width adjustment. The method described.       5. A method according to claim 4, further comprising the step of generating an image for the 2D screen by further projector means.       8. The method of claim 7, further comprising using a reflector to direct a projectiono beam from the switchable projector means to the display surface.       The method of claim 1, further comprising the steps of defining a finite space of a second skewed coordinate system and a second 2D screen of the volumetric 3D display, and corresponding steps of coordinate system mapping and image display. A method for displaying a geometric primitive with a desired level of brightness in an actual 3D space of a volumetric 3D display, wherein the geometric primitive is a straight line or a surface and displaying the volumetric 3D display or volumetric 3D image. Including a spatially distributed display element for the method,
(1) determining a minimum amount Nge_op of the required display elements to display the geometric primitive with full brightness Br_op;
(2) Based on the following relationship:
(Nge / Nge_op) x (Bge / Bge_f) = Br / Br_op,
Determining a desired display element quantity Nge for displaying the geometric primitive at a desired luminance level, wherein Br represents the desired luminance level of the geometric primitive, and Bge_f is the full luminance of the display element Said level, wherein Bge represents the level of brightness of said display element to be used in rendering said geometry
(3) drawing the geometric primitive using the amount of the desired display element;
Including said method. The step of determining a minimum amount of the display element comprises determining a reference amount Ns_op of a sample point and a maximum pixel expansion number N_d to represent the geometric basis with full luminance;
The step of determining the amount of the desired display element comprises [(Nsxn_pd) / (Ns_op x N_d)] x (Bge / Bge_f) = Br / Br_op, based on the following relationship:
Determining a desired sample point quantity Ns and a desired pixel dilation number n_pd to represent the geometric primitive,
Drawing the geometric primitive;
(I) distributing the amount of the desired sample points in the geometric basis and obtaining the coordinates of the desired sample points by calculation;
(Ii) rendering the calculated sample points using the desired pixel dilation number;
The method of claim 10. The geometric base is a straight line,
The step of determining a reference amount of the sample point comprises:
(A) obtaining, by calculation, the minimum amount of sample points required to fill the straight line with the display elements in three perpendicular directions;
(B) selecting the highest of the three smallest amounts calculated from step (a) as the reference amount Ns_op;
Distributing the desired amount of sample points includes distributing sample points evenly on the straight line;
The method of claim 11. The geometric shape is a surface;
The sample points are distributed between one or more auxiliary surfaces, the auxiliary surfaces closely stack with the spacing between adjacent auxiliary surfaces;
The step of determining the reference amount Ns_op includes the step of determining the optimal amount of sample points for each auxiliary surface, wherein the optimal amount of sample points represents the auxiliary surface with full brightness, and the optimal amount of all the auxiliary surfaces Is equal to Ns_op,
The step of determining the desired amount Ns comprises selecting a specified amount of sample points for each auxiliary surface, the sum of the sample points of all the auxiliary surfaces being equal to Ns;
The step of dispensing the desired amount of sample points includes the step of dispensing the specified amount of sample points to each corresponding auxiliary surface;
The method of claim 11. Further comprising the step of determining a minimum value of the spacing based on the orientation and position of the surface with respect to the spatial distribution of display elements such that display elements corresponding to adjacent sample points do not overlap.
The method of claim 13. The surface is a triangular surface and the auxiliary surface is also a triangle;
Determining the optimal amount of sample points for each auxiliary surface;
(A) determining an optimum number of sample points for each of the three edges of the auxiliary surface, the optimum number of sample points required to fill the edge with the display element at full brightness; Said step being a minimum amount of
(B) defining an end having an optimal number Ns_op_d of directional edges and highest sample points and defining an edge having a base edge and an optimal number of lowest sample points Ns_op_b;
(C) determining an optimal amount of sample points on the auxiliary surface based on the value Ns_op_d x Ns_op_b / 2,
The step of selecting a specified amount of sample points for each auxiliary surface determines the number Ns_d of sample points at the direction end and the number Ns_b of sample points at the base end, and based on the value Ns_d x Ns_b / 2 Including the step of determining a specified amount of sample points of
The step of dispensing the specified amount of sample points to each auxiliary surface;
(A) calculating the coordinates of the Ns_d sample point at the direction end and the coordinates of the Ns_b sample point at the base end by calculation;
(B) The mesh system on the auxiliary surface conceptually draws a straight line from each sample point at the edge of the base, makes the straight line parallel to the end of the direction, and draws a straight line from each sample point at the end of the direction And assembling by making the straight line parallel to the edge of the base,
(C) placing sample points at each intersection of mesh lines falling within the auxiliary surface;
The method of claim 13. The step of determining the minimum amount of said display element comprises:
(I) calculating the geometric base intersection with a slice of a frame, wherein the intersection includes a small bitmap, and each pixel of the small bitmap includes one of the display elements Said step,
(Ii) stitching the intersection together into a composite bitmap;
(Iii) completely rendering the composite bitmap with full luminance, comprising the step of having a total number of pixels Np_CBM_f in the composite bitmap;
The step of determining the amount of the desired display element is based on the following relationship: (Np_CBM / Np_CBM_f) × (Bge / Bge_f) = Br / Br_op
Determining a desired number of pixels Np_CBM for rendering the composite bitmap as described above;
Drawing the geometric primitive;
(I) redrawing the composite bitmap using the desired number of pixels;
(Ii) rendering the intersection according to a redrawn composite bitmap;
The method of claim 10. The luminance level is a luminance level of one of the primary colors;
11. The method of claim 10, further comprising the step of displaying a geometric base to display the geometric base of a desired color level with other primary color brightness levels. A method for displaying a surface having a monochromatic texture map on a volumetric 3D display, wherein the volumetric 3D display includes a spatially distributed display element for displaying a volumetric 3D image. ,
(1) dividing the full intensity scale of the texture map into a number of different intensity ranges, wherein each intensity range corresponds to a different region of the texture map;
(2) establishing a mapping from each region of the texture map to a corresponding region of the surface;
(3) assigning a luminance ratio to each corresponding area of the surface based on the intensity range of the area according to the mapping, wherein the luminance ratio is defined as a desired luminance ratio to full luminance Said step,
(4) drawing the corresponding respective areas of the surface of different density of display elements to represent different luminance ratios.       The step of drawing each corresponding region of the surface includes the step of distributing sample points at a desired point density and the step of dilating each of the sample points into a desired number of display elements, The method of claim 18, wherein the combination of dilations represents a luminance ratio of the region. The surface is a triangular surface;
The sample point distribution step comprises:
a. Assembling a mesh system for placing sample points, wherein the mesh system has a mesh density required to draw the triangular surface with a luminance ratio equal to the luminance ratio of the corresponding region; Step,
b. 20. The method of claim 19, comprising placing sample points only at intersections of mesh straight lines within corresponding said regions according to a mesh system. Assigning a region index to each pixel of the texture map and establishing a data structure of the region index in the texture map with respect to the position of the corresponding pixel, wherein the region index is one of the regions according to a pixel intensity range. Said step indicating one,
A step of ratio mapping of said mesh system to a map of texture;
Checking whether mesh line intersections fall within corresponding areas of the surface by use of the area index data structure;
21. The method of claim 20, further comprising: The monochromatic texture map is one place of a color texture map;
Further comprising the step of displaying the surface having a map of textures of other primary colors to display the surface with a map of the color texture.
The method of claim 18. The volumetric 3D display includes spatially distributed display elements;
The texture mapping includes a procedure for displaying a surface having a monochromatic texture map, or
(1) dividing the full intensity scale of the texture map into a number of different intensity ranges, wherein each intensity range corresponds to a different region of the texture map;
(2) establishing a mapping from each region of the texture map to a corresponding region of the surface;
(3) assigning a luminance ratio to each corresponding area of the surface based on the intensity range of the area according to the mapping, wherein the luminance ratio is defined as a desired luminance ratio to full luminance Said step,
4. The method of claim 3, comprising the step of: (4) rendering each corresponding region of the surface of another density of display elements to represent another luminance ratio.       The step of drawing each corresponding region of the surface includes the step of distributing sample points at a desired point density and the step of dilating each of the sample points into a desired number of display elements, The method of claim 23, wherein the combination of dilations represents a luminance ratio of the region. The step of determining the number Ns_d and the number Ns_b includes:
(A) calculating the two numbers based on a triangular surface orientation with respect to the structure of the display element; and (b) fitting the two numbers to approximately equally spaced meshes in two directions of rendering. 16. The method of claim 15, comprising. A method of displaying a 3D volume having a monochromatic intensity scale distribution in the actual 3D space of the volumetric 3D display, wherein the volumetric 3D display includes spatially distributed display elements, ,
(1) dividing the full intensity scale of the 3D volume into a number of different intensity ranges, wherein each intensity range corresponds to a different spatial region of the 3D volume;
(2) assigning a luminance ratio, BR, to each of the spatial regions of the 3D volume based on a corresponding intensity range of the spatial region, wherein the luminance ratio is a desired luminance to full luminance Said step, defined as the ratio of
(3) rendering each corresponding spatial region of the 3D volume of a different density of display elements to represent a different luminance ratio,
(A) assembling a reference mesh system and selecting a reference dilation number N_d, the mesh system including intersecting mesh lines for placing sample points, wherein the reference mesh system samples to a reference point density Providing a reference mesh density for placing points, wherein the reference point density can render a full 3D volume with full brightness when each of the sample points corresponds to N_d display elements;
(B) Based on the following relationship:
[(Ns x n_pd) / (Ns_op x N_d)] x (Bge / Bge_f) = BR of the spatial area
Assembling a desired mesh system and selecting a desired expansion number n_pd, where Ns represents the number of sample points for rendering the entire 3D volume using the desired mesh system, Each sample point corresponds to an n_pd display element, Ns_op represents the number of sample points for rendering the entire 3D volume using the reference mesh system, and Bge_f represents the full brightness level of the display element. Said step, wherein Bge represents the level of brightness of a display element to be used in rendering;
(C) placing sample points only at locations within the spatial region according to the desired mesh system and the desired dilation number;
Said step comprising:
Including said method. The 3D volume comprises 3D data volume pixels;
(I) assigning each said volume pixel a regional index, wherein said regional index indicates a corresponding spatial region in the range of intensity of said volume pixel;
(Ii) setting up the regional index data structure with respect to the position of the volume pixel of the 3D volume;
(Iii) mapping between the desired mesh system and a 3D volume, wherein each intersection of the mesh lines corresponds to one volume pixel of a 3D volume;
(Iv) checking whether mesh line intersections fall within the spatial region by using the regional index data structure;
27. The method of claim 26, further comprising: The 3D volume comprises 3D data volume pixels;
(I) assigning each said volume pixel a regional index, wherein said regional index indicates a corresponding spatial region in the range of intensity of said volume pixel;
(Ii) setting up the regional index data structure with respect to the position of the volume pixel of the 3D volume;
(Iii) mapping between volume pixels of the same region index and a desired mesh system of the corresponding spatial region, wherein each said volume pixel corresponds to one or more intersections of said mesh line;
27. The method of claim 26, further comprising: The monochromatic intensity scale is one field of the color intensity scale;
Further comprising the step of displaying the 3D volume with a brightness scale of other primary colors to display the 3D volume at a desired color level;
27. The method of claim 26. Defining a scan box in a 3D volume of space;
A step of defining a small 3D volume corresponding to the space covered by the scan box,
A step of displaying the original 3D volume of the reduced luminance ratio;
Rendering and displaying the aforementioned small 3D volume;
27. The method of claim 26, further comprising:

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