USRE42534E1 - Bicubic surface real-time tesselation unit - Google Patents
Bicubic surface real-time tesselation unit Download PDFInfo
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- USRE42534E1 USRE42534E1 US12/767,997 US76799710A USRE42534E US RE42534 E1 USRE42534 E1 US RE42534E1 US 76799710 A US76799710 A US 76799710A US RE42534 E USRE42534 E US RE42534E
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
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- the present invention relates to computer graphics, and more specifically to a method and apparatus for rendering bicubic surfaces in real-time on a computer system.
- Object models are often stored in computer systems in the form of surfaces.
- the process of displaying the object generally requires rendering, which usually refers to mapping the object model onto a two dimensional surface. At least when the surfaces are curved, the surfaces are generally subdivided or decomposed into triangles in the process of rendering the images.
- a cubic parametric curve is defined by the positions and tangents at the curve's end points.
- a Bezier curve as shown in FIG. 5 for example, is defined by a geometry matrix of four points (P 1 -P 4 ) that are defined by the intersections of the tangent vectors at the end points of the curve. Changing the locations of the points changes the shape of the curve.
- Cubic curves may be generalized to bicubic surfaces by defining cubic equations of two parameters, s and t.
- bicubic surfaces are defined as parametric surfaces where the (x,y,z) coordinates in a space called “world coordinates” (WC) of each point of the surface are functions of s and t, defined by a geometry matrix P comprising 16 control points ( FIG. 5 ).
- x f(s,t)
- y g(s,t)
- z h(s,t) s ⁇ [0,1], t. ⁇ [0,1], where ⁇ represents an interval between the two coordinates in the parenthesis.
- Textures described in a space called “texture coordinates” (TC) that can be two or even three dimensional are described by sets of points of two ((u,v)) or three coordinates ((u,v,q)).
- texture coordinates TC
- FIGS. 1A and 1B are diagrams illustrating a process for rendering bicubic surfaces.
- the principle used for rendering such a curved surface 10 is to subdivide it into smaller four sided surfaces or tiles 12 by subdividing the intervals that define the parameters s and t. The subdivision continues until the surfaces resulting from subdivision have a curvature, measured in WC space that is below a predetermined threshold.
- This subdivision induces a subdivision of the TC, for each pair of parameters (si,tj) we obtain a pair (u i,j , v i,j ) (or a triplet (u i,j , v i,j , q i,j )).
- ui,j a(si,tj)
- vi,j b(si,tj)
- a Cartesian point called “vertex” in WC, Vi,j (f(si,tj),g(si,tj),h(si,tj)).
- a special type of texture called displacement map having the pair (p,r) as coordinates can be used to generate special lighting effects.
- For each pair of parameters (si,tj) we also obtain an index pair (pi,j ri,j) that index a displacement value (dxi,j, dyi,j, dzi,j). for the vertex Vi,j.
- each such resultant four-sided surface 12 is then divided into two triangles 14 (because they are easily rendered by dedicated hardware) and each triangle surface gets the normal to its surface calculated and each triangle vertex also gets its normal calculated. The normals are used later on for lighting calculations.
- each vertex or triangle plane normal needs to be transformed when the surface is transformed in response to a change of view of the surface, a computationally intensive process that may need dedicated hardware. Also, there is no accounting for the fact that the surfaces are actually rendered in a space called “screen coordinates” (SC) after a process called “projection” which distorts such surfaces to the point where we need to take into consideration the curvature in SC, not in WC.
- SC screen coordinates
- FIG. 2 shows an architecture of a conventional computer graphics system, including the architecture of a graphics processing unit (GPU).
- a CPU 1 executes a software application in the form of a game play or a physical or chemical simulation, etc., in which objects to be rendered are represented as triangle meshes in an object database stored in memory.
- the triangle meshes are transmitted over an accelerated graphics port (AGP) bus 6 to the GPU 5 , which is typically part of a display adapter (video card).
- the AGP bus 6 is a high-speed port that is designed for the display adapter only to provide a direct connection between the card and memory.
- the GPU 5 includes a transform unit 2 , a lighting unit 3 and a renderer unit 4 .
- the object modeling in the application is executed on parametric surfaces such as nurbs, Bezier, splines, and the surfaces are subdivided or tessellated off-line and stored as triangle vertices in a triangle database by means of commercially available tools, such as the Alias suite.
- the triangle vertices are then transmitted from the CPU 1 (the triangle server) to the GPU 5 (the rendering engine) at the time for rendering. Previous attempts to execute the tessellation in hardware in real-time have not been successful because of the severe limitations of the implementation so the current state of the art has been off-line tessellation.
- the composing triangles may appear very large and the object looses its smoothness appearance, looking more like a polyhedron.
- the increase in the scene complexity has pushed up the number of triangles, which has pushed up the demands for higher bus bandwidth.
- the bus 6 that connects the CPU 1 with the GPU 5 has increased 8 ⁇ in frequency, from AGP 1 ⁇ to AGP 8 ⁇ in the PC space in the last few years. There are physical constraints in terms of signal propagation that preclude the continuation of the frequency increase in bus design.
- Moreton from Nvidia has resurrected the real-time tesselation unit described in the U.S. Pat. No. 6,597,356 entitled “Integrated Tesselator in a Graphics Processing Unit,” issued Jul. 22, 2003. Moreton's invention doesn't directly tesselate patches in real-time, but rather uses triangle meshes pre-tesselated off-line in conjunction with a proprietary stitching method that avoids cracking and popping at the seams between the triangle meshes representing surface patches. His tesselator unit outputs triangle databases to be rendered by the existing components of the 3D graphics hardware.
- the present invention provides a graphics processing unit for rendering objects from a software application executing on a processing unit in which the objects to be rendered are received as control points of bicubic surfaces.
- the graphics processing unit includes a transform unit, a lighting unit, a renderer unit, and a tessellate unit for tessellating both rational and non-rational object surfaces in real-time.
- FIGS. 1A and 1B are diagrams illustrating a process for rendering bicubic surfaces.
- FIG. 2 describes the current architecture of a computer graphics system, in specific the current architecture of a graphics processing unit (GPU).
- GPU graphics processing unit
- FIG. 3 describes the new architecture of a GPU that includes a Tessellator Unit inserted between the Transform Unit and the Light Unit.
- FIG. 4 describes the architecture of an internet system employing multiple CPU's at the receiving end performing real-time tessellation.
- FIG. 5 illustrates a bicubic surface
- FIG. 6 describes the recursive subdivision of the convex hull of a Bezier curve.
- FIG. 7 describes the texture mapping process.
- FIG. 8 illustrates the recursive subdivision of the convex hull of a bicubic surface.
- FIG. 9 shows how to calculate one criterion for terminating the subdivision.
- FIG. 10 shows how cracks can appear at the T-joints on the boundary curves between surfaces.
- FIG. 11 shows how to “zipper” the cracks at the T-joints.
- FIG. 12 shows how using the same subdivision for neighboring surfaces completely avoids the cracks.
- FIG. 13 shows an example of a strip of surfaces.
- FIG. 14 shows an example of a fan of surfaces.
- FIG. 15 shows an example of a mesh of surfaces.
- the present invention is directed to a method and apparatus for minimizing the number of computations required for the subdivision of bicubic surfaces into triangles for real-time tessellation.
- the following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. Various modifications to the preferred embodiment will be readily apparent to those skilled in the art and the generic principles herein may be applied to other embodiments. Thus, the present invention is not intended to be limited to the embodiment shown but is to be accorded the widest scope consistent with the principles and features described herein.
- U.S. Pat. No. 6,563,501 by the Applicant of the present application, provides an improved method and system for rendering bicubic surfaces of an object on a computer system.
- Each bicubic surface is defined by sixteen control points and bounded by four boundary curves, and each boundary curve is formed by boundary box of line segments formed between four of the control points.
- the method and system include transforming only the control points of the surface given a view of the object, rather than points across the entire bicubic surface.
- a pair of orthogonal boundary curves to process is selected. After the boundary curves have been selected, each of the curves is iteratively subdivided, as shown in FIG. 6 , wherein two new curves are generated with each subdivision. The subdivision of each of the curves is terminated when the curves satisfy a flatness threshold expressed in screen coordinates, whereby the number of computations required to render the object is minimized.
- the method disclosed in the '501 patent minimizes the number of computations required for rendering of an object model by requiring that only two orthogonal curves of the surface be subdivided, as shown in FIG. 8 .
- the entire rendering process can potentially be performed in real-time.
- the computations for subdivision are performed by expressing the criteria of terminating the subdivision in the screen coordinates (SC).
- SC screen coordinates
- the curvature is estimated based on how flat it appears to be in SC (pixels), rather than how curved it is in WC, the number of computations required may further be minimized.
- the possibility of rendering images in real-time is further enhanced.
- allowing the curvature to be measured in SC units also allows for accommodating the distance to the viewer, thus giving the process an “automatic level of detail” capability.
- the present invention utilizes the above method for minimizing the number of computations required for the subdivision of bicubic surfaces into triangles in order to provide an improved architecture for the computer graphics pipeline hardware.
- the improved architecture replaces triangle mesh transformation and rendering with a system that transforms bicubic patches and tesselates the patches in real-time. This process is executed in a real-time tesselation unit that replaces the conventional transformation unit present in the prior art hardware 3D architectures.
- the reduction in computations is attained by reducing the subdivision to the subdivision on only two orthogonal curves.
- the criteria for sub-division may be determined in SC.
- the description is provided with reference to Bezier surfaces for illustration. Due to such features, the present invention may enable objects to be subdivided and rendered in real-time.
- the partition into triangles may also be adapted to the distance between the surface and the viewer resulting in an optimal number of triangles. As a result, the effect of automatic level of detail may be obtained, whereby the number of resulting triangles is inversely proportional with the distance between the surface and the viewer.
- the normals to the resulting tiles are also generated in real-time by using the cross product of the vectors that form the edges of the tiles.
- N′ i,j N i,j +dN i,j /*displace the normal for bump mapping*/
- V′ i,j V i,j +(dx i,j , dy i,j , dz i,j )*N i,j /*displace the vertex for displacement mapping*/
- bump and displacement mapping are executed in the renderer, pixel by pixel for all the points inside each triangle */
- FIG. 3 a block diagram of the graphics system of the present invention is shown, where like components from FIG. 2 have like reference numerals.
- the present invention utilizes the above algorithm to provide an improved graphics system 10 .
- the system 10 includes CPU 1 and GPU 7 .
- the GPU 7 includes a transform unit 2 , a lighting unit 3 , a renderer unit 4 , and a tessellate unit 9 coupled between the transform unit 2 and the lighting unit 3 for tessellating both rational and non-rational object surfaces in real-time.
- the CPU 1 executes a software application and transmits over the AGP bus 6 the object database expressed in a compressed format as control points of the bicubic surfaces.
- the control points of the bicubic surfaces are transformed by the transform unit 2 , and then the surfaces are tessellated into triangles by the tessellate unit 9 .
- the tessellate unit 9 executes the microcode described above in the Step 1 through Step 4 , thereby affecting the real-time tessellation.
- the vertices of the triangles are then lit by the lighting unit 3 and the triangles are rendered by the renderer unit 4 executing steps 5 through 7.
- FIG. 4 is a diagram illustrating architecture of a network-based graphics system targeting for performing real-time tessellation for online gaming according to a second preferred embodiment of the present invention.
- This second embodiment targets the interactive multi-player game play over a network, such as the Internet in which multiple client computers 14 comprising a CPU 1 and GPU 5 are in communication with a server 12 .
- the server 12 sends object databases over the Internet in the form of control points for bicubic patches to the CPUs 1 for tessellation of the databases into triangles.
- the CPUs 1 then transfer the triangles to conventional GPU's 5 comprising transform units 2 , lighting units 3 and renderer units 4 .
- it is the CPUs 1 that execute the microcode steps 0 though 4 described above to effect the real-time tessellation. Note, that the CPUs 1 also execute Step 0, the transformation of the control points.
- ⁇ ⁇ DL ⁇ 8000 4400 2420 1331 ⁇
- ⁇ ⁇ DR ⁇ 0242 1331 0044 0008 ⁇
- N i,j P i ⁇ 1,j P i,j ⁇ P i,j P i,j+1 /length(P i ⁇ 1,j P i,j ⁇ P i,j P i,j+1 )
- Such a surface lies within a convex hull formed by its control points.
- P 11 through P 44 Similar to the Bezier surfaces.
- the surface lies within the convex hull formed by P 11 thru P 44 .
- p is the order
- N i,p (s) are the B-spline basis functions
- P i are control points
- the curve lies within the convex hull formed by the control points.
- the subdivision of the surface reduces to the subdivision of the convex hull of the boundary curves or of the internal curves as described in the case of the Bezier surfaces.
- n is a number expressed in pixels or fraction of pixels.
- artifacts may be produced with n starting at 1, especially along a silhouette.
- Starting values for n may also include 0.5 and n>1, for reasons of rapid prototyping and previewing.
- a more general criterion is provided: Maximum ⁇ distance (P 22 to line (P 42 , P 12 ), distance (P 32 to line (P 42 , P 12 ) ⁇ *2d/(P 42 z+P 12 z) AND Maximum ⁇ distance (P 33 to line (P 43 , P 13 ), distance (P 23 to line (P 43 , P 13 ) ⁇ *2d/(P 43 z+P 13 z) ⁇ n
- the above criterion is the most general criterion and it will work for any class of surface, both rational and non-rational. It will also workfordeformable surfaces. It will work for surfaces that are more curved along the boundary or more curved internally. Since the curvature of deformable surfaces can switch between being boundary-limited and internally-limited the flatness of both types of curves will need to be measured at the start of the tesselation associated with each instance of the surface.
- the pair of orthogonal curves used for tesselation can then be one of: both boundary, both internal, one boundary and one internal.
- the subdivision termination criteria may be used for the control of the numerically controlled machines.
- the criterion described below is calculated in object coordinates.
- “tol” represents the tolerance, expressed in units of measurement (typically micrometers) accepted for the processing of the surfaces of the machined parts:
- cracks may appear at the boundary between abutting patches. This is mainly due to the fact that the patches are subdivided independently of each other. Abutting patches may and do exhibit different curvatures resulting into different subdivisions. For example, in FIG. 10 we see that the right-hand patch has a finer subdivision than the left-hand one. At the boundary we see how a “T-joint” has been formed. When rendering the parallel strips of triangles to the left and to the right of the common boundary a crack may become visible in the area of the T-joint.
- One of the approaches disclosed herein exhibits identical straight edges for the two patches sharing the boundary.
- the other implementation exhibits even stronger continuity; the subpatches generated through subdivision form continuous strips orthogonal to the shared boundary. This is due to the fact that abutting patches are forced to have the same parametric subdivision.
- the present invention provides two different crack prevention methods, each employing a slightly different subdivision algorithm.
- FIG. 10 shows how the triangle strip on the right side of the boundary curve produces a vertex (a “T-joint”) inside the edge of a triangle belonging to the strip on the left of the boundary.
- the “T-joint” has been removed by connecting two edges that emerge from the vertex that originated the “T-joint”.
- the present invention provides a Graphics Utility Library (GLU).
- GLU Graphics Utility Library
- the GLU includes several different types of primitives including, strips, fans, meshes, and indexed meshes of surface patches.
- the first patch contributes 16 vertices, each subsequent patch contributes only 12 because 4 are shared with the previous patch.
- S 1 only 4
- the corners P 11 , P 14 , P 41 , P 44 have color and texture attributes
- the remaining 12 have only geometry attributes.
- Si in the strip only one
- P 44 has color and texture attributes.
- each patch has only 3 boundary curves, the fourth boundary having collapsed to the center of the fan.
- the first patch in the strip enumeration has 11 vertices, each subsequent patch having 8.
- Vertex P 11 listed first in the fan definition, is the center of the fan and has color and texture attributes in addition to geometric ones.
- the first patch, S 1 has two vertices with color and texture attributes, P 41 and P 44 ; the remaining 9 have only geometric attributes.
- Each subsequent patch, Si has only one vertex with all the attributes.
- the anchor patch, S 11 has 16 vertices, all the patches in the horizontal and vertical strips attached to S 11 have 12 and all the other patches have 9.
- a further embodiment of the present invention provides a method for accelerating rendering.
- a well known technique used for accelerating rendering is backface culling, which a method which discards triangles that are facing away from the viewer. It is beneficial to extend this technique to cover backfacing surfaces. This way, we avoid the computational costs of tesselating surfaces that face away from the user. Our proposed method discards such surfaces as a whole, before even starting the tesselation computation.
- the convex hull is made up of 13 planar side panels ( ⁇ P 41 ,P 44 ,P 43 ,P 42 ⁇ , ⁇ P 44 ,P 34 ,P 33 ,P 43 ⁇ , . . . ⁇ P 33 ,P 23 ,P 22 ,P 32 ⁇ ) and one bottom panel ( ⁇ P 44 ,P 41 ,P 11 ,P 14 ⁇ ) that may not be planar in most cases.
- the order of listing the vertices in each of the 14 panels coincides with the outwards pointing normal. If any of the 13 side panels is front facing than the surface may be (at least partially) front facing. Therefore, the criterion for culling the patch as backfacing is:
- the patch should not be culled. This criterion means that since the bottom panel ⁇ P 44 , P 41 , P 11 , P 14 ⁇ is backfacing, there may be other panels in the convex hull that may be front facing. This being the case, the patch should not be considered as being backfacing and should not be culled.
- a method and system has been disclosed for performing tessellation in real-time in a GPU.
- Software written according to the present invention is to be stored in some form of computer-readable medium, such as memory or CD-ROM, or transmitted over a network, and executed by a processor.
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Abstract
Description
u=a(s,t) v=b(s,t) (and q=c(s,t))
-
- Transform the 16 control points and the single normal that determine the surface
-
- curve bounding box is below a certain predetermined number of pixels as measured in screen coordinates.
L1=P1
L2=(P1+P2)/2
H=(P2+P3)/2
L3=(L2+H)/2
R4=P4
R3=(P3+P4)/2
R2=(R3+H)/2
R1=L4=(L3+R2)/2
Vi,j=V(x(si,tj),y(si,tj),z(si,tj)) i=1,m, j=1,n
Ni,j=Pi−1,jPi,j×Pi,jPi,j+1/length(Pi−1,jPi,j×Pi,jPi,j+1)
N′i,j=Ni,j+dNi,j/*displace the normal for bump mapping, pixel by pixel in the renderer section */
P′i,j=Pi,j+(dxi,j, dyi,j, dzi,j)*Ni,j/*displace the point P for displacement mapping, pixel by pixel */
S(s,t)=[Σm i=1Σn j=1Ni,p(s)Nj,q(t)wi,jPi,j]/Σm i=1Σn j=1Ni,p(s)Nj,q(t)wi,j
C(s)=[Σm i=1Ni,p(s)wi,jPi]/Σm i=1Ni,p(s)wi
where p is the order, Ni,p(s) are the B-spline basis functions, Pi are control points, and with the weight of is the last ordinate of the homogeneous point. The curve lies within the convex hull formed by the control points.
Maximum {distance (P12 to line (P11, P14), distance (P13 to line (P11, P14)}*2d/(P12z+P13z)<n
Maximum {distance (P24 to line (P14, P44), distance (P34 to line (P14, P44)}*2d/(P24z+P34z)<n
where n is a number expressed in pixels or fraction of pixels. However, artifacts may be produced with n starting at 1, especially along a silhouette. Starting values for n may also include 0.5 and n>1, for reasons of rapid prototyping and previewing.
Maximum {distance (P22 to line (P42, P12), distance (P32 to line (P42, P12)}*2d/(P42z+P12z) AND
Maximum {distance (P33 to line (P43, P13), distance (P23 to line (P43, P13)}*2d/(P43z+P13z)<n
Maximum {distance (P22 to line (P21, P24), distance (P23 to line (P21, P24)}*2d/(P21z+P24z) AND
Maximum {distance (P32 to line (P31, P34), distance (P33 to line (P31, P34)}*2d/(P31z+P34z)<n
Maximum {distance (P12 to line (P11, P14), distance (P13 to line (P11, P14)}*2d/(P12z+P13z) AND
Maximum {distance (P42 to line (P41, P44), distance (P43 to line (P41, P44)}*2d/(P42z+P43z)<n
Maximum {distance (P24 to line (P14, P44), distance (P34 to line (P14, P44)}*2d/(P24z+P34z) AND
Maximum {distance (P21 to line (P11, P41), distance (P31 to line (P11, P41)}*2d/(P11z+P41z)<n
Claims (20)
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US22210500P | 2000-07-28 | 2000-07-28 | |
US09/734,438 US6563501B2 (en) | 2000-07-28 | 2000-12-11 | Bicubic surface rendering |
US10/436,698 US20030189570A1 (en) | 2000-07-28 | 2003-05-12 | Bicubic surface rendering |
US10/732,398 US7245299B2 (en) | 2003-05-12 | 2003-12-09 | Bicubic surface real-time tesselation unit |
US11/778,515 US7532213B2 (en) | 2000-07-28 | 2007-07-16 | Bicubic surface real time tesselation unit |
US12/767,997 USRE42534E1 (en) | 2000-07-28 | 2010-04-27 | Bicubic surface real-time tesselation unit |
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US9779547B2 (en) | 2013-07-09 | 2017-10-03 | Samsung Electronics Co., Ltd. | Tessellation method for assigning a tessellation factor per point and device performing the method |
US20240020935A1 (en) * | 2022-07-15 | 2024-01-18 | The Boeing Company | Modeling system for 3d virtual model |
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