CN117058300B - Method for calculating intersection point of acceleration ray and uncut curved surface based on KD tree - Google Patents
Method for calculating intersection point of acceleration ray and uncut curved surface based on KD tree Download PDFInfo
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Abstract
The invention discloses a method for calculating intersection points of acceleration rays and uncut curved surfaces based on KD trees, which belongs to the field of ray tracing cut curved surfaces and comprises the following steps: step S1: trimming the annular curve into a curve section and a curve unit; step S2: and (3) establishing a spatial hierarchy structure based on the curve set obtained in the step S1. By improving the kd-Tree data structure algorithm in the flow of tracking NRUBS curved surfaces of rays, subdividing a two-dimensional space by using a space area heuristic algorithm and accelerating a curve searching flow based on the subdivision, the method can be better utilized on a modern GPU with a dynamic curved surface subdivision function, so that the quantity of rays projected on the GPU can reach real-time performance of tens of thousands to hundreds of millions of rays per second in a complex scene containing hundreds of thousands of NURBS curved surfaces and clipping curves.
Description
Technical Field
The invention relates to the technical field of ray tracing cutting NURBS curved surfaces, in particular to a method for accelerating intersection point calculation of rays and uncut curved surfaces based on a simplified KD tree.
Background
Ray tracing is a widely used method in computer graphics to trace rays in a three-dimensional scene and calculate their intersection with the surface of an object. Ray tracing has become one of the criteria for many three-dimensional applications because it can provide high quality images.
The trimmed NURBS surface is a most commonly used modeling mode in the field of geometric modeling, and the number of modeling by using the method is rapidly increased in recent years;
Ray tracing has become a rapidly evolving method of generating computer-real graphical images of geometric models.
Through retrieval, the chinese patent of application number CN116310048a discloses a method for calculating the intersection point of ray tracing and NURBS curved surface based on curvature subdivision, which proposes the problem of accurately displaying any shape that can be generated by a modeling system if ray tracing can be implemented on NURBS curved surface, and improves the tessellation algorithm in flow 2 of ray tracing NRUBS curve and NURBS curved surface to accelerate the flow of finding the intersection point of ray tracing and NURBS curve and curved surface.
However, NURBS surfaces are powerful mathematical tools that can uniformly represent surfaces of various forms such as planes, quadrics, beta splines, and beziers, a 3D model is typically represented by a set of basic NURBS surfaces and a set of clipping curves when represented by clipped NURBS surfaces, using clipped NURBS surfaces to represent geometric models has become an industry standard, and rendering of surfaces is typically solved by tessellation and z-buffer rendering in some applications such as CAD, however, such rendering methods are prone to visible artifacts because fixed rendering can result in highlighting of triangle edges;
Furthermore, the triangle mesh may become very large and occupy a lot of memory. Therefore, the ray tracing calculation of NURBS curved surfaces is difficult to realize in real-time performance due to the large calculation complexity and the like, and thus has not been widely used in industry.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a method for calculating intersection points of acceleration rays and uncut curved surfaces based on a KD tree.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
A method for accelerating intersection point calculation of light rays and uncut curved surfaces based on KD trees comprises the following steps:
step S1: trimming the annular curve into a curve section and a curve unit;
step S2: establishing a space hierarchical structure based on the curve set obtained in the step S1, wherein the outermost layer is correspondingly a kd tree, the inner layer consists of kd leaves containing curve sets, and each curve set contains a curve unit array;
Step S3: the method comprises the steps that overlapped minimization processing is carried out on kd trees constructed on a curve set through a priority queue algorithm, so that the calculation cost is reduced;
Step S4: subdividing all leaf nodes in the kd tree to optimize the calculation cost;
step S5: the evaluation cost of the whole leaves of the curve set is reduced by the blank region segmentation.
Further, in step S2, the kd-tree is constructed from top to bottom, dividing the empty leaves into inside or outside the curve, the complete information of the leaves containing all trimmed curve elements and initial parity, the surface area of all full leaf nodes representing the probability of passing the parity test, wherein:
for the constructed kd-Tree, the cost of the search is:
Where SA is the surface area of the 2D space, SA leaf,i is the surface area of the ith leaf bounding box, |N leaf,i | is the number of curves contained in the leaf, C test is the cost of the horizontal ray and curve intersection test, SA inner,i is the surface area of the internal node, C trav is the cost of traversing the internal nodes of the tree, C test and C trav include access time to the data, thus minimizing the memory consumed by the kd-Tree in a computer architecture, but making it difficult to evaluate the cache on the GPU.
Further, in step S3, the curve set is further subdivided only by the maximum overlapping area, and the cost function used is reduced to the sum of the surface areas overlapping with the other curve sets, a ij, by:
C(Si)＝∑j≠iAij
The priority queue selects the curve set with the highest cost for subdivision, and the subdivision process will be terminated if any further curve set subdivision results in a smaller total combined area.
Further, in step S4, after the kd-tree is built, the conditions for subdividing the full leaf nodes are specifically:
the presence leaf contains two or more curves/curve sets;
The presence of a large leaf surface area increases the likelihood of parity testing use, and thus increases the cost of use.
Further, in step S4, the leaf L may be further subdivided using spatial median values along the longer sides of the bounding box, the curves/curve sets associated with L being distributed to the two child nodes according to their intersection with the bounding boxes of the newly created left and right child nodes, provided that the refinement is performed in particular:
the first condition is: based on the relative surface area of L relative to the entire kd-tree surface area, a threshold ratio r SA =0.0006 is used;
The second condition is: based on length, if the long side of the L bounding box is too small relative to the diagonal of the entire kd-tree bounding box, the leaves cannot be subdivided, using a threshold length ratio of r l =0.025, where the values of r SA and r l are determined by extensive searching of the test scene.
Further, in step S5, by finding the maximum blank area of the leaf, specifically:
if the area is large enough compared to the surface area of the entire leaf, a new internal node is inserted, wherein the empty leaf represents a blank space;
When o/h > r cutoff is satisfied, a blank region division method is applied, where o/h is the blank region area relative to the leaf area.
Compared with the prior art, the invention has the beneficial effects that:
The method comprises the steps of improving a kd-Tree data structure algorithm in a light tracking NRUBS curved surface process, subdividing a two-dimensional space by using a space area heuristic algorithm, and accelerating a curve searching process based on the following three methods: 1. overlapping and minimizing the kd-Tree constructed on the curve set by a priority queue algorithm; 2. optimizing the computation cost by subdividing all leaf nodes in the kd-tree; 3. the evaluation cost of the whole leaves of the curve set is reduced through the blank region segmentation, and the improvement of the light ray tracking speed on the GPU can be achieved. The method can be better utilized on a modern GPU with a dynamic surface subdivision function, so that the quantity of rays projected on the GPU can reach real-time performance of tens of thousands to hundreds of millions of rays per second in a complex scene containing hundreds of thousands of NURBS surfaces and clipping curves.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is a flow chart of a method for calculating intersection points of acceleration rays and uncut curved surfaces based on KD trees;
FIG. 2 is a flow chart of a simplified version of kd-Tree acceleration ray tracing in an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
In the application, a method for calculating the intersection point of a simplified version of accelerated ray and an unclamped curved surface based on a kd tree is provided based on the steps of a kd tree method for carrying out ray tracing on a NURBS curved surface.
Examples:
referring to fig. 1-2, a method for accelerating intersection point calculation of a ray and an unclamped curved surface based on a KD-tree includes the following steps:
step S1: trimming the annular curve into a curve section and a curve unit;
It should be noted that the loop trimming curve is a series of curve segments with subsequent boundary points, and the curve segments may be subdivided into curve units, for example, at local extremum points or inflection points. If local extrema are used for subdivision, the curve segments created are monotonic.
The ring clipping curve consists of a series of curve sets, wherein a single curve set contains a series of curve units with the same monotonicity.
Step S2: establishing a space hierarchical structure based on the curve set obtained in the step S1, wherein the outermost layer is correspondingly a kd tree, the inner layer consists of kd leaves containing curve sets, and each curve set contains a curve unit array;
Step S3: the method comprises the steps that overlapped minimization processing is carried out on kd trees constructed on a curve set through a priority queue algorithm, so that the calculation cost is reduced;
Step S4: subdividing all leaf nodes in the kd tree to optimize the calculation cost;
step S5: the evaluation cost of the whole leaves of the curve set is reduced by the blank region segmentation.
Referring to fig. 2, in a preferred embodiment of the present application, in step S2, the kd-tree is constructed from top to bottom, dividing the empty leaves into inside or outside the curve, the complete information of the leaves containing all trimmed curve units and initial parity, and the surface area of all full leaf nodes representing the probability of passing the parity test, wherein:
for the constructed kd-Tree, the cost of the search is:
Where SA is the surface area of the 2D space, SA leaf,i is the surface area of the ith leaf bounding box, |N leaf,i | is the number of curves contained in the leaf, C test is the cost of the horizontal ray and curve intersection test, SA inner,i is the surface area of the internal node, C trav is the cost of traversing the internal nodes of the tree, C test and C trav include access time to the data, thus minimizing the memory consumed by the kd-Tree in a computer architecture, but making it difficult to evaluate the cache on the GPU.
It should be further noted that the overall cost function of the kd-tree and the cost function in 3D ray tracing have some similarity, but also vary greatly. Since the rectangular surface area given by the leaves of the kd-tree represents only geometric probabilities, the 2D search starting from bounding box rectangles on the kd-tree is computationally expensive and traverses only to the first leaf during point location search. Thus, the surface area of a 2D search can accurately represent the geometric probability assuming that the search is uniformly distributed. The cost function of ray tracing uses a local greedy approach in the kd-tree construction process, leveraging object counts to balance the work on both sides of the splitting plane. For the case of 2D, there is no object, but it is the length of the left and right curves of the segmentation plane that represents the cost of evaluation. In fact, the computational cost corresponds to the length of the curve segment in the box;
kd-trees are curve units constructed using bounding boxes to represent curve segments or sets of curves, and access to all leaves during a search after a leaf is created requires expensive parity computation costs.
In a specific embodiment of the application, in step S3, the curve set is further subdivided only by the maximum overlap area, and the cost function used is reduced to the sum of the surface areas overlapping the other curve sets, a ij, by:
C(Si)＝∑j≠iAij
The priority queue selects the curve set with the highest cost for subdivision, and the subdivision process will be terminated if any further curve set subdivision results in a smaller total combined area.
It should be further noted that the curve set is inserted into the priority queue along with its initial cost, and the most costly curve set is checked at the top of the priority queue.
Based on the monotonicity of each curve set along U and V, a simple binary search can be performed, and each monotonic curve set Si can be further subdivided in preprocessing using a cost function:
c= Σc (S i) is the calculation time taken to evaluate whether a point is in the shape under the assumption that the kd-tree is not built, To traverse the cost of the kd-tree, this cost is unknown in this preprocessing step and is therefore considered constant;
The probability of performing binary search in the curve set is obtained by the ratio of the surface area of the boundary frame of the curve set to the surface area of the boundary frame of the whole kd-tree;
to cost searching in the curve set, the method is characterized by/> Calculated, where |S i | is the number of cells in the curve set, and c read is the cost of reading the bounding box from memory;
The probability of parity test is calculated by emitting horizontal rays in the box of any element of the curve set, and the probability is calculated by the sum of the surface area of the single curve set unit boundary box and the surface area of the boundary box of the whole kd-tree;
The cost of parity test is the average cost of reading the curve set unit data; /(I) Calculated from the surface area at which the bounding boxes of S i and S j intersect.
The set of curves comprising N curve elements is subdivided into all possible N-1 configurations, with the configuration selected for minimal cost.
If it is assumed that the cost of subdividing a curve set into two new smaller curve sets is less than the cost of not subdivision, then the curve set subdivision is accepted. The original curve set is removed from the priority queue and two newly created smaller curve sets are inserted into the priority queue. This process continues until subdivision is possible, so that the cost of the search is minimized.
In a specific embodiment of the present application, after the kd-tree is built in step S4, the conditions for subdividing the full leaf nodes are specifically:
the presence leaf contains two or more curves/curve sets;
The presence of a large leaf surface area increases the likelihood of parity testing use, and thus increases the cost of use.
Referring to fig. 2, in a particular embodiment of the application, in step S4, the leaf L may be further subdivided using spatial median values along the longer sides of the bounding box, the curves/sets of curves associated with L being distributed to the two child nodes according to their intersection with the bounding box of the newly created left and right child nodes, provided that:
the first condition is: based on the relative surface area of L relative to the entire kd-tree surface area, a threshold ratio r SA =0.0006 is used;
The second condition is: based on length, if the long side of the L bounding box is too small relative to the diagonal of the entire kd-tree bounding box, the leaves cannot be subdivided, using a threshold length ratio of r l =0.025, where the values of r SA and r l are determined by extensive searching of the test scene.
It should be noted that, according to the number of curve sets, a preprocessing step is performed, and the curve sets and the rectangular bounding boxes of each unit are used for pruning the search in the calculation process;
After preprocessing, a kd-Tree is constructed on the curve set using a surface area heuristic, so that traversing the point locations from the root of the kd-Tree is minimized, and finally, the leaves of each kd-Tree are cast a horizontal ray to the left and the calculated parity test is stored in the leaves.
After the data structure is built, point location searches are performed on points (U, V) on the 2D parameter domain, and the pruning algorithm first traverses the kd-tree down from the root until a leaf is found. If the leaves of the kd-tree are empty, the result is then classified as either external or internal based on pre-computed values (parity tests) stored in the leaves. If the leaf contains one or more curve sets and the points (U, V) are within the bounding box of the curve set, then a binary search is used to find the corresponding curve set unit to be tested; if the points (U, V) are within the bounding box of the curve set unit, the correct result must be calculated by emitting rays to the left; if the point (U, V) is outside the bounding box of the curve set, the correct result is determined by the mutual position of the point (U, V) with respect to the bounding box of the curve set.
For other curve sets in the kd-tree leaves, the results are put together as the sum of the intersecting boundary crossings, and the rules of parity testing are again used.
As a preferred embodiment of the present application, in step S5, by finding the maximum blank area of the leaf, specifically:
if the area is large enough compared to the surface area of the entire leaf, a new internal node is inserted, wherein the empty leaf represents a blank space;
when o/h > r cutoff is satisfied, applying a blank region segmentation method, wherein o/h is the blank region area relative to the leaf area;
Referring to fig. 2, in the present embodiment, by widely searching for a range of meaningful values, it is found that r cutoff =0.075 is a more reasonable value for the current GPU architecture.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (5)
1. The method for calculating the intersection point of the acceleration ray and the uncut curved surface based on the KD tree is characterized by comprising the following steps:
step S1: trimming the annular curve into a curve section and a curve unit;
Step S2: establishing a space hierarchical structure based on the curve sets obtained in the step S1, wherein the outermost layer is correspondingly a kd tree, the inner layer consists of kd leaves containing the curve sets, each curve set contains a curve unit array, and the complete information of the leaves contains all curve units and initial parity;
step S3: the method for reducing the calculation cost by carrying out overlapping minimization treatment on the kd-Tree constructed on the curve set through a priority queue algorithm specifically comprises the following steps:
The curve sets are subdivided only by the maximum overlap area, and the cost function used is the sum of the surface areas of each curve set that overlap with the other curve sets:
C(Si)＝∑j≠iAij
Selecting the curve set with the highest cost for subdivision by a priority queue algorithm, wherein the subdivision process is terminated if any further curve set subdivision results in a smaller total combined area;
Step S4: subdividing all leaf nodes in the kd tree to optimize the calculation cost;
step S5: the evaluation cost of all leaf nodes of the curve set is reduced by blank region segmentation.
2. The method of claim 1, wherein in step S2, the KD-tree is constructed from top to bottom, dividing the empty leaf into inside or outside the curve, and the surface area of all leaf nodes represents the probability of passing the parity test, wherein:
for the constructed kd-Tree, the cost of the search is:
Where SA is the surface area of the 2D space, SA leaf,i is the surface area of the ith leaf bounding box, |N leaf,i | is the number of curves contained in the leaf, C test is the cost of the horizontal ray and curve intersection test, SA inner,i is the surface area of the internal node, C trav is the cost of traversing the internal node of the tree, and C test and C trav include access times to the data.
3. The method of claim 2, wherein in step S4, after constructing the KD-tree, the conditions for subdividing all leaf nodes are specifically:
the presence leaf contains two or more curves/curve sets;
there is a large leaf surface area, which increases the cost of use.
4. The method of claim 3, wherein in step S4, when the leaf L satisfies the following conditions, the curve/curve set associated with L is further subdivided using spatial median along the long sides of the bounding box, and the conditions for refinement are specifically:
the first condition is: based on the relative surface area of L relative to the entire kd-tree surface area, a threshold ratio r SA =0.0006 is used;
The second condition is: based on length, if the diagonal ratio of the long side of the L bounding box to the entire kd-tree bounding box is less than the threshold length ratio r 1 =0.025, the leaves cannot be subdivided, where the values of r SA and r 1 are determined by extensive searching of the test scene.
5. The method of claim 4, wherein in step S5, by finding the maximum blank area of the leaf, the method is as follows:
If the maximum empty region is o/h > r cutoff compared to the surface area of the entire leaf, then an empty region segmentation method is applied, inserting new internal nodes, where the empty leaf represents an empty space.
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| US8188997B2 (en) * | 2000-06-19 | 2012-05-29 | Mental Images Gmbh | Accelerated ray tracing using shallow bounding volume hierarchies |
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