JP2799048B2 - Display method of object trajectory in three-dimensional space - Google Patents

Description

Description: BACKGROUND OF THE INVENTION The present invention relates to a method for displaying a trajectory of an object including a fluid moving in a three-dimensional space, and more particularly to a three-dimensional method for simultaneously displaying spatial position and time information of the trajectory. The present invention relates to a display method of a spatial object trajectory.

[Conventional technology]

2. Description of the Related Art Graphical display of a moving object such as an aircraft flying in the air, a flying object such as a missile, a tornado generated and moving in the air, or a torpedo or a ship moving in water. Further, in a coal-fired thermal power plant, heat recovery has recently been performed from exhaust gas having a higher dust level than before, from the viewpoint of energy saving. Therefore, the problem of wear of the heat recovery device due to dust has arisen, and the demand for improving the dust collecting performance of the dust separator has been increasing. Also, with the increase in coal use,
In order to cope with problems such as classification and wear in a mill, it has become necessary to clarify and understand the behavior of fine particles. In response to this requirement, it is difficult to accurately grasp the behavior of particles such as dust in a model experiment or a test of an actual machine. Therefore, a computer simulation method has been developed.

Although the particle orbit analysis method has been known for a long time, analysis in a gas flow idealized by a simple system is often common.
By the way, recent advances in flow analysis technology have been remarkable, and the analysis of considerably complicated flows has become possible to some extent. Hereinafter, a method for analyzing behavior of particles combined with a flow analysis method will be described. In addition, in addition to a three-dimensional flow, there are various shapes of particles, and collision of particles can be considered. Here, a two-dimensional flow is assumed to be a spherical particle shape, and a dust separator with relatively few collisions is used. Show application.
The way of thinking and processing is the same for three dimensions.

Outline of analysis method Fig. 21 shows the analysis procedure. Particle trajectory analysis is based on the assumption that gravity, buoyancy, drag due to the relative velocity of gas and particles, and lift due to rotation of particles act on spherical particles. It is like that. First, only the gas flow is calculated, and in this gas flow field, particles are ejected from each part of the entrance of the apparatus, and the trajectory is tracked. First, the shape of the analysis area, the inlet gas flow rate, etc. are given as inputs, and "gas flow analysis" is performed by solving the flow analysis and the Navier-Stokes equation, which is the basic equation, and the velocity vectors at each position are obtained as output. . In addition, input the particle size, specific gravity, and calculation start position of the particles, and perform “particle motion analysis”.
The position of each time particle is obtained as an output. Finally, a particle trajectory diagram is obtained by using this output as an input and performing a “particle trajectory diagram creation” process. The present invention relates to this last process.

Gas flow analysis In the case of a two-dimensional incompressible steady flow, the basic equation of flow is Na
The vier-Stokes equation and the equation of continuation 4 are expressed as follows in the orthogonal xy coordinate system.

Where V _x : flow velocity in the x-axis direction (m / s) V _y : flow velocity in the y-axis direction (m / s) ν: kinematic viscosity coefficient (m ² / s) ρ _g : gas density (kg / m ³ ) P : Pressure (P _a ) △: Labracian flow function (ψ)-According to vorticity (ω) method, (1)-
Equation (3) is transformed as follows.

Δψ = ω (5) where By solving the equations (4) and (5), the gas flow velocity at each point in the flow field can be obtained. Here, (4)
The difference method can be used for the expression, and the Ikegawa method using the finite element method can be used for the expression (5) (Int.J.Numeri
eal Melhods in Eng. 14 103-113 (1979)).

Particle Orbit Analysis As shown in FIG. 22, when a spherical particle having a mass m flies at a velocity V in a gas flow having a flow velocity V _g , Depends on gas flow Works, and the equation of motion is expressed by the following equation.

When this is divided by m, the following equation is obtained.

Where m = πD _P ³ ρ _P / 6 (9) here, If the equation (8) is expressed in the xy orthogonal coordinate system, the equation of motion of the particle is as follows.

The subscripts x and y represent components in the x and y axis directions, respectively.
Also, the drag coefficient C _D takes the next value by a range of particle Reynolds number R _e.

here, By solving equation (14), the trajectory and velocity of the particles can be obtained. Here, a minute time Δt is set, the particle velocity ΔV and the moving distance Δl within this time are obtained, and the procedure is repeated to obtain the trajectory and velocity of the particles.

Visualization and display of the particle trajectories obtained in this way are performed.

Conventional particle trajectory display technology (wire display) Fig. 23 shows a drawing example using the conventional display technology by wire (single line) display. In this example, since there is no information on the depth direction, three-dimensional grasp cannot be performed. FIG. 24 shows a drawing example of the same trajectory viewed from another viewpoint, in which it is difficult to determine which side is on the viewpoint side at the intersection. If you look closely at the two figures, you may understand, but it is quite difficult.

In addition, there is no information on the residence time and velocity of the particles, and they are not known at all. (Particle tracer display) Recently, it is frequently used especially in animation display and stereo (stereoscopic) display.

Fig. 25 shows an example of particle tracer display.
This is the trail of smoke coming out of the chimney. There are a method of representing particles by points, a method of representing particles by spheres, and the like. When a large number of particles are to be blown at once, there is also an example in which the starting position or the range is color-coded so as to know where the particles came from.

This method is difficult to understand if there are many particles in a still image as shown in FIG. 25, and animation display is suitable. In addition, three-dimensional movement is easy to understand even in a still image by using stereo display. In addition, since particles are drawn at regular intervals, it can be understood that the flow rate is slow in a dense area and fast in a sparse area.

(Ribbon display) "A Study of the Evolution"
of Numerically Modeled Severe Storm: RBWilhelmso
n Other: International Journal of Super Computing Aplli
In cations, 1990, there are two cases where local storms and tornado growth were numerically simulated and animated. One is a ribbon display of the particle trajectory. The three groups of red ribbons and the blue ribbons with different starting points show the behavior in the tornado and the animation of the three-dimensional graphics. ing. Since the ribbon elongates with time, the speed can be roughly determined by the speed, and the three-dimensional shape can be determined by the shaded display of the ribbon surface.

The other is to visualize the rotation of the wind, which is displayed by adding a twist like a screw to the ribbon. In other words, this is an expression method in which the arrow gradually rotates and rotates as an animation image.

[Problems to be solved by the invention]

In the above prior art, no consideration is given to expressing the three-dimensional position of an object (particle) trajectory and its time on a normal still image, and thus a two-dimensional expression method in which the time is unclear in a still image. Could not plot the particle trajectory, and there was insufficient information to use it for technical studies. On the other hand, the use of animation requires enormous cost and time, making it impossible to use in daily design and development research work. Further, the stereo display has a high facility cost and a limitation of using special glasses, and thus cannot be copied and bound in a report.

An object of the present invention is to provide a method that eliminates such inconveniences and visualizes the three-dimensional positional relationship of an object (particle) trajectory and its time using a still image that can be displayed on a normal CRT screen.

[Means for solving the problem]

The above object can be achieved by a ribbon display of an object (particle) trajectory in which a color is applied every unit time and a shaded surface is displayed. That is, the problem of the prior art is that, in the method of displaying the movement trajectory of the object in the three-dimensional space, the step of inputting the three-dimensional position data of the trajectory at predetermined time intervals, Interpolating a trajectory; calculating a curvature vector of the trajectory at a predetermined position based on the trajectory data obtained in the input step and the interpolation step; and a predetermined width perpendicular to the curvature vector at the curvature vector calculation point. A method of displaying an object trajectory in a three-dimensional space, comprising the steps of: forming a ribbon surface of the same and changing the color of the formed ribbon surface at predetermined time intervals; Inputting three-dimensional position data of a trajectory at predetermined time intervals, interpolating a trajectory between adjacent positions indicated by the data, A step of obtaining a curvature vector of a trajectory at a predetermined position based on the trajectory data obtained in the input step and the interpolation step, and a step of forming a ribbon surface having a predetermined width parallel to the curvature vector at a point at which the curvature vector is calculated, Displaying the formed ribbon surface in different colors at predetermined time intervals. A method for displaying an object trajectory in a three-dimensional space, the method for displaying a movement trajectory of an object in a three-dimensional space Inputting three-dimensional position data of a trajectory at a predetermined time interval, calculating a curvature vector at a predetermined position based on the trajectory data obtained in the step, and setting a predetermined width perpendicular to the curvature vector. Forming a ribbon surface, displaying the formed ribbon surface in different colors at predetermined time intervals, and displaying the object trajectory in a three-dimensional space.
In a method of displaying a movement trajectory of an object in a three-dimensional space, inputting three-dimensional position data of a trajectory at predetermined time intervals, interpolating a trajectory between adjacent positions indicated by the data, Calculating a curvature vector at a predetermined position based on the trajectory data obtained in the step and the interpolation step; trajectory data obtained in the input step and the interpolation step; and using the curvature vector to generate an object trajectory at predetermined time intervals. In a method of displaying a trajectory of an object in a three-dimensional space and a method of displaying a trajectory of a moving object in a three-dimensional space, the method displays a curvature vector at a predetermined position while displaying a wire in a different color. A step of inputting three-dimensional position data of a trajectory at each time interval, a step of interpolating a trajectory of an adjacent positional relationship indicated by the data, and a step of inputting trajectory data obtained in the two steps. The object trajectory is a rod-shaped body having a predetermined cross-sectional shape based on the data,
And changing the surface color at predetermined time intervals for display. The method of displaying an object trajectory in a three-dimensional space is characterized in that:

[Action]

By separately applying the ribbon every unit time, it can be easily understood that if the color section is short, the particles are slow, and if the color section is long, the particles are fast. Also, the number of this section is the total residence time of the particle.

Also, when a plurality of ribbons or even one ribbon is entangled with confidence by the hidden surface display, it is clear which one is in front and the three-dimensional configuration between the trajectories can be understood.

Further, since the surface of the ribbon is shaded, it can be understood that a three-dimensional curved movement of the particle trajectory can be taken.

The above graphic display can be displayed as a still image on an ordinary graphics display, and can be easily printed on paper as a color hard copy, so that it can be used in daily engineering work.

〔Example〕

An embodiment of the present invention will be described with reference to the flow of FIG.

What is the large structure in Fig. 1? The calculation of the ribbon surface generation is performed _Tmax times, which is the total number of the particle trajectories (therefore, the number of ribbons is _Tmax ), and then the display processing is performed.

 Hereinafter, the procedure for generating the ribbon surface will be described.

In step 1, data of a particle trajectory is first read. This is the spatial position data of the particles at each calculation time interval ΔT It is. Here, i is the ribbon number, n is the number of the time section, 0 ≦ n ≦ N _div , and N _div is the maximum section number. 1A
The figure shows how to make n universal.

In step 2, next, parametric spline interpolation is performed. The parametric spline represents a free curve in a three-dimensional space, and uses a parameter (parameter) that does not depend on the x, y, and z coordinates of the space. The method of deriving the equation is described in Fujio Yamaguchi: Shape Processing Engineering [I]:
This is described in detail in Banyusha (1982).

As shown in FIG. 2, the expression of the spline function in the section between points Q _n-1 and Q _n is defined as P _n (t), 0 ≦ t ≦ 1, with t as a parameter. According to this formula, discrete points Q of the particle trajectory can be continuously and smoothly connected. That is, since the calculation points of the originally smooth particle trajectory are output as discrete points Q, they can be smoothly connected using the spline function formula.

In step 3, a curve vector is determined. Its purpose is to determine the orientation of the face of the ribbon. In other words, the particle trajectory is simply a trajectory of a line and never forms a plane. But,
In the present invention, it is necessary to use a ribbon display for hidden surface shading display (hidden surface display: making the rear surface invisible, and shading display: giving a shadow and three-dimensional appearance). Therefore, we considered how it is reasonable to determine the surface direction of the ribbon. As a result, it was concluded that it is most reasonable to set the direction of the ribbon surface as the direction of the curvature vector of the locus curve.

Here, the direction of the ribbon surface is as shown in FIG.
Vectors perpendicular to the plane of the ribbon in small sections of the ribbon for drawing. On the other hand, the curvature vector is a reciprocal of the curvature radius ρ of the absolute value, that is, a smaller radius has a larger value. The direction is a vector toward the center of curvature. By matching the two, the three-dimensional curve of the locus when the locus is displayed as a ribbon can be better understood by the shaded surface.

Here, the method of finding the curvature vector K is very simple because the second derivative of the curve P is K.

In K = P ″ 5, the coordinate values of the four corners of the surface in each minute section of the ribbon are determined and the surface is clearly defined.In advance of 4, the counter (COUNTER) for separately applying the ribbon in the second speed is cleared to zero. , And set the initial color to the display color (COLOR).
In this flow, two different colors are assigned to each locus so that the color can be changed for each locus (for each ribbon).

In 9, per data entire section N _div, repeat the above process.

Further, as shown by 10 in each section, the processing is repeated M _div times so that the trajectory can be displayed smoothly.
In the example of FIG. 3, M _div = 12.

The generation of the ribbon surface in the minute section in the step 5 is the third step.
In this figure, the coordinates of four vertices of the surface surrounded by the solid line are determined. The end points P (t−Δt) and P (t) on the trajectory and the curvature vector (= surface direction) K on the trajectory in the minute section of the ribbon are obtained by using the equation of P. The coordinates of the four vertices of the surface can be easily obtained.

Next, switching of face colors will be described. As shown in FIG. 6, COUNTER is increased by one for each minute section.

When the value of COUNTER reaches CLRSW (color switching interval) as shown at 7, COUNTER is cleared to zero as shown at 8 and the display color COLOR is changed to another color number. Here, CLRSW * △ t is a section in which one color is continuous. For example, if this section is 1 second, the total number of ribbon stripes becomes the number of seconds. Step 8
MOD (1, COLOR + 1) indicates that the operation is (1) if (COLOR + 1) is odd and 0 if (COLOR + 1) is even. All coordinate values and display colors of the minute section plane calculated as described above are stored.

In steps 11 and 12, the entire surface of the ribbon is hidden and shaded and displayed on the screen. This process is not specific to the present invention, but is a general process, and a detailed description thereof will be omitted.

FIG. 4 shows a display example of the particle trajectory represented by the flow of FIG. 1 of the present invention. This is a display example using exactly the same data as shown in FIG. 23 and viewed from the same viewpoint.

In the above-described embodiments, an example is shown in which the movement trajectory data of the object is input at regular intervals of ΔT time.
The time ΔT can be changed to a desired value and input. Also, the embodiment has been described in which the trajectory between adjacent positions based on the input trajectory data is interpolated. However, if the trajectory data input interval (ΔT) of the first object is appropriately set, this interpolation processing step is omitted. Can be.

As described above, according to the present invention, since the particle trajectory is displayed in different colors for each unit time, the speed and the total residence time depending on the location of the particles can be easily known.

Further, by using the ribbon surface, the front-rear positional relationship of the locus and the direction of the curvature can be three-dimensionally and easily understood.

Although two ribbon colors are used, it is within the scope of the present invention to use three colors or to insert a dividing line every unit time. Is a merit that here in two colors, the number c of combinations for selecting two colors from N color was _{c = nC 2, N = 4,5,6,7,8} ...... contrast, c = 6,
10, 15, 21, 28,..., More combinations can be made than in the single color display, and it is easy to distinguish a plurality of trajectories.

Further, even if the number of particle trajectory data is not so large, the trajectory can be drawn smoothly due to the parametric spline interpolation. Since the calculation of the main body and the particle trajectory is performed at very fine time intervals, if all of them are output, the number of calculation points becomes 10,000 or more. On the other hand, at least about 1000 points are required to connect the calculation points with a straight line to make them look smooth. On the other hand, in this embodiment, several tens to 100 points can be displayed with equal or higher quality, and the data amount can be significantly reduced.

As another embodiment, a method of obtaining a curvature vector without using parametric spline interpolation will be described.

FIG. 5 shows a method of obtaining a curvature vector from a circle passing through three points. The direction from the center of the three points toward the center of the circle is defined as the direction of the curve, and the reciprocal of the radius of the circle is defined as the absolute value of the curvature vector. Then, the curvature vector between the points Q _n−1 and Q _n is used by interpolating K _n−1 and K _n .

According to this method, although the number of required data points is large, the calculation of a parametric spline is unnecessary, and the program development is easy.

An even easier embodiment is shown in FIG. For example, when obtaining the curvature vector at Q _n, 2 points from _{Q n, Q n-1,} Q n + 1
Are drawn perpendicularly to the line segment connecting the lines and in a direction intersecting the line segment, and the direction is defined as a curvature vector. Since the magnitude of the curvature vector is not necessary to determine the orientation of the ribbon surface,
The above processing is sufficient. If the data points are close enough, Thus, the directions of _Kn obtained in this way are three points, Q _n−1 ,
It is almost toward the center of the circle passing through Q _n and Q _{n + 1} .

 Next, another embodiment of the display method will be described.

FIG. 7 is a particle trajectory obtained using the implementation flow of FIG. Based on this, another embodiment will be described.

FIG. 8 shows a plane vector defined at right angles to the curvature vector, and expresses the same information as in FIG.

FIG. 9 shows a ribbon having a narrow width at a high speed and a wide width at a low speed, so that the flow velocity can be illustrated more clearly.

An embodiment in which the ribbon width is changed according to the flow rate will be described with reference to FIG. In the example shown, the time from Q _{n -1} to Q _n and Q
Time from _m-1 to Q _m are the same, showing a case of creating a ribbon surface is divided both into four sections. Attention is paid to one surface which is a drawing unit of the ribbon. The upstream width ( _{Wt- [ Delta] t} ) of this minute surface is known from the calculation of the minute surface before it, and the downstream width ( _Wt ) is unknown.

Here, Δl = | P (t) −P (t−Δt) | That is, the distance between these two points and the area of the minute surface ΔA =
(Constant) It is. Transform this, This formula determines the width of the ribbon on the downstream side of the minute surface.
By drawing using the ribbon width obtained in this way, a portion with a high trajectory speed can be made thin and a portion with a low trajectory speed can be made thick. Alternatively, the ribbon width at a high speed may be widened and the ribbon width at a low speed may be narrowed.

FIG. 10 is also referred to as a tape measure display, in which a time scale is put on the ribbon. In addition, the total residence time is indicated by numbers. FIG. 11 is obtained by superimposing arrows indicating speed vectors on FIG.

FIG. 12 is an example in which a cylinder is used without using a ribbon. In this case, it takes longer to display than the ribbon, but it is not necessary to calculate the curvature.

FIG. 13 shows a wire display instead of a ribbon, with a plate indicating the surface direction per unit time, and the number of display surfaces is small and the display is fast. This may be a ball instead of a plate.

FIG. 14 is a drawing in which a curvature vector is simultaneously drawn with respect to a wire display. In this case, the color of the display wire is changed and displayed at predetermined time intervals as in the case of the ribbon display. Since this display is only a line, the display processing is fast, and is suitable for examination by an expert.

FIG. 15 is a display obtained by adding a curvature vector to the display of FIG. 7, and is a display with much information.

In FIG. 16, particles flowing out of the analysis area are indicated by arrows,
Particles hitting a wall are displayed without arrows. FIG. 17 shows a translucent display so that when there are a plurality of trajectories, the trajectory on the rear side can be seen.

FIG. 18 shows an example in which one edge is changed in color and emphasized so that the twist is easy to understand in the case of display in consideration of the rotation of the particles. For the same purpose, it is possible to change the color of the front and back of the ribbon.

In FIG. 19, the color is displayed lighter as the distance from the viewpoint increases, giving a sense of depth. In the above embodiment,
Although the display example of the particle trajectory has been described, the present invention naturally covers the trajectory of the flow of the fluid in the three-dimensional space, the trajectory of the flying object in the atmosphere, and the trajectory of the object traveling in the water.

Although the present invention is intended for a still image, if it is used for animation display and stereo display, an image that is much easier to understand can be obtained.

In addition, the present invention can be widely used not only for particle trajectories, but also for displaying behaviors having dimensions of space and time, such as displaying routes of automobiles, ships, airplanes, rockets, and the like, and displaying trajectories of electron beams and elementary particles.

〔The invention's effect〕

According to the present invention, information on the three-dimensional position and time of an object trajectory can be displayed in one diagram, which is effective for understanding the behavior of an object and also effective for use in presentation.

The present invention can be used commonly for still images, animation displays, and stereoscopic displays. When used as a still image, display processing is fast because there is only one figure, and drawing can be performed almost in real time, which is suitable for engineering studies. In addition, paper copies and photographs can be used as part of the report, and the cost is extremely low.

The present invention provides visualization of a trajectory having dimensions of space and time,
It can be widely used not only for object trajectories.

[Brief description of the drawings]

1 is a system diagram of an embodiment of the present invention, FIG. 1A is an explanatory diagram of assigning particle trajectory calculation section numbers, FIG. 2 is an explanatory diagram of spline function processing connecting between calculation points of the particle trajectory, and FIG. 4A, 4B, 4D, 4D, 4D, and 4D, the plane directions and coordinates of minute parts in a trajectory data section.
FIGS. 5 and 6 are explanatory views of another method for obtaining a curvature vector of a particle trajectory according to the present invention. FIGS. 7 to 20 are display examples of a particle trajectory according to the present invention. Figure,
FIG. 21 is a diagram showing the calculation procedure of the conventional particle trajectory, FIG. 22 is a diagram showing the principle of the conventional particle trajectory calculation, FIG. 23 and FIG. FIG. 26 is an example of a conventional particle tracer display, and FIG. 26 is an example of a ribbon display according to the prior art. 1 ... particle trajectory data reading step 2 ... parametric spline interpolation step 3 ... curvature vector calculation step 4
…… Initial color setting and zero setting process of color change counter,
5: minute section ribbon surface generation step, 6: counter step for each minute section, 7: face color switching determination, 8: face color switching, 9: repetition processing step within all sections, 10: within each section Repetitive processing step, 11 ... shading processing of the entire surface, 12 ... display step.

Continuation of the front page (72) Inventor Masanori Ozaki 1-2-10 Isogo, Isogo-ku, Yokohama-shi, Kanagawa Prefecture Inside of Yokohama Laboratory, Babcock Hitachi, Ltd. (58) Field surveyed (Int.Cl. ⁶ , DB name) G06T 15 / 00-15/70 G06F 17/50

Claims (9)

(57) [Claims] 1. A method for displaying a movement trajectory of an object in a three-dimensional space, wherein three-dimensional position data of a trajectory at predetermined time intervals is input, and a trajectory between adjacent positions indicated by the data is interpolated. A step of calculating a curvature vector of a trajectory at a predetermined position based on the trajectory data obtained in the input step and the interpolation step; and at a calculation point of the curvature vector, a ribbon surface having a predetermined width perpendicular to the curvature vector. A method for displaying an object trajectory in a three-dimensional space, comprising: a forming step; and a step of displaying the formed ribbon surface by changing a color at predetermined time intervals. 2. The method according to claim 1, wherein the step of displaying the ribbon surface includes displaying the formed ribbon surface in different colors at predetermined time intervals, and moving the object on the ribbon surface at each time interval. A method of displaying an object trajectory in a three-dimensional space, wherein a vector display is performed. 3. The ribbon surface display step according to claim 1, wherein the formed ribbon surface is displayed by changing the color at predetermined time intervals, and the curvature vector at the position is displayed on the display ribbon surface. A method for displaying a trajectory of an object in a three-dimensional space, characterized in that: 4. A method for displaying a movement trajectory of an object in a three-dimensional space, wherein three-dimensional position data of a trajectory at predetermined time intervals is input, and a trajectory between adjacent positions indicated by the data is interpolated. A step of obtaining a curvature vector of a trajectory at a predetermined position based on trajectory data obtained in the input step and the interpolation step; and forming a ribbon surface having a predetermined width parallel to the curvature vector at a calculation point of the curvature vector. And displaying the formed ribbon surface in a different color at predetermined time intervals.
A method for displaying an object trajectory in a three-dimensional space. 5. The method according to claim 1, wherein the width of the ribbon surface is controlled according to the moving speed of the object trajectory when forming the ribbon surface at the curvature vector calculation point. Of displaying an object trajectory in a three-dimensional space. 6. A method for displaying a movement trajectory of an object in a three-dimensional space, comprising the steps of: inputting three-dimensional position data of the trajectory at predetermined time intervals, and at a predetermined position based on the trajectory data obtained in said step. Calculating the curvature vector, forming a ribbon surface having a predetermined width perpendicular to the curvature vector, and displaying the formed ribbon surface in different colors at predetermined time intervals. Display method of object trajectory in space. 7. Claims (1), (2), (3), (4),
(5) In (6), the display step of the formed ribbon surface is a step of performing a shadow shading process on the ribbon surface and changing the color at predetermined time intervals for display. A method for displaying an object trajectory in a three-dimensional space. 8. A method for displaying a movement trajectory of an object in a three-dimensional space, wherein three-dimensional position data of the trajectory at predetermined time intervals is input, and a trajectory between adjacent positions indicated by the data is interpolated. A step of calculating a curvature vector at a predetermined position based on the trajectory data obtained in the input step and the interpolation step; a trajectory data obtained in the input step and the interpolation step; and an object trajectory using the curvature vector. Is displayed in a wire with a different color every predetermined time, and a curvature vector is displayed at a predetermined position.
A method for displaying an object trajectory in a three-dimensional space. 9. A method for displaying a movement trajectory of an object in a three-dimensional space, wherein three-dimensional position data of a trajectory at predetermined time intervals is input, and a trajectory between adjacent positions indicated by the data is interpolated. And a step of displaying the object trajectory as a rod-shaped body having a predetermined cross-sectional shape based on the trajectory data obtained in both steps, and changing the surface color at predetermined time intervals. A method for displaying an object trajectory in a three-dimensional space.