WO2000004433A2 - Systeme et procede permettant de creer des hierarchies de volume englobant par le biais de la simplification de modele - Google Patents

Systeme et procede permettant de creer des hierarchies de volume englobant par le biais de la simplification de modele Download PDF

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Publication number
WO2000004433A2
WO2000004433A2 PCT/SG1999/000078 SG9900078W WO0004433A2 WO 2000004433 A2 WO2000004433 A2 WO 2000004433A2 SG 9900078 W SG9900078 W SG 9900078W WO 0004433 A2 WO0004433 A2 WO 0004433A2
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Prior art keywords
hierarchy
sub
component
objects
bounding volume
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PCT/SG1999/000078
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English (en)
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WO2000004433A3 (fr
Inventor
Tiow Seng Tan
Ket Fah Chong
Kok Lim Low
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National University Of Singapore
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Priority to US09/743,921 priority Critical patent/US6747651B1/en
Publication of WO2000004433A2 publication Critical patent/WO2000004433A2/fr
Publication of WO2000004433A3 publication Critical patent/WO2000004433A3/fr

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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
    • G06T17/005—Tree description, e.g. octree, quadtree

Definitions

  • the present invention relates generally to computer graphics and virtual reality. More specifically, the invention relates to systems and methods for generating bounding volume hierarchies for use in the checking of collisions among objects in complex interactive computer environments or in ray tracing computation to generate photo-realistic computer images.
  • the present invention is a method for processing an arbitrary collection of objects, in a simulated computer environment, into hierarchies of bounding volumes.
  • the following teachings are most relevant to the present invention:
  • bounding volume hierarchies are also utilized to accelerate ray tracing process to generate photo-realistic computer images (see
  • any given sub-tree in the hierarchy should contain objects that are near each other; (ii) the bounding volume of each node should be minimal; (iii) the sum of all bounding volume should be minimal; and (iv) the construction of the tree should concentrate on the nodes nearer the root of the tree. To date, finding close to optimal hierarchy remains a partially solved problem.
  • the current invention exploits shape information obtainable from simplified models to partition input model into its natural components so as to generate effective bounding volume hierarchy.
  • the inventive method includes first a step of generating simplified models; second, deriving various components of the input model from clues in simplified models; third, joining various components into a hierarchy to form the top few levels of the eventual bounding volume hierarchy; and then finally partitioning parts of each minimal sub-component into the bounding volume hierarchy.
  • This invention can be used to build a software system or an apparatus that generates effective bounding volume hierarchies for checking collision in interactive computer applications or for ray tracing process to generate photorealistic images.
  • Such software systems may already have methods to construct simplified models for the same application and, thus, overhead due to simplification needed by the present invention is insignificant.
  • the inventive system is a framework that can incorporate other existing methods within its various embodiments.
  • This invention may also take the form of an article of manufacture. More specifically, the article of manufacture is a computer-usable medium, including a computer-readable program code embodied therein wherein the computer- readable code causes a computer to execute the inventive method.
  • the invention is very careful in creating a hierarchy with all necessary considerations mentioned in Kay and Kajiya (1986). In particular, in the handling of the top-most few levels of the hierarchy in that they are a natural partition of the input model.
  • the current invention provides a framework that manages input models in a middle-in way to perform bottom-up to find the top few levels of the bounding volume hierarchy and top-down to find the lower levels.
  • the middle-in approach is possible with the partitions derived through simplified models.
  • This two-level structure capitalizes on the best features of both traditional top-down and bottom-up approaches, and can incorporate existing acceleration techniques applicable to both approaches.
  • the invention described herein satisfies the above-identified needs in the prior art by providing solutions.
  • the invention provides methods and apparatuses to efficiently generate a good bounding volume hierarchy of an input computer environment to be utilized in collision detection in interactive 3D computer applications, such as computer simulations and computer games, and in ray tracing processes to generate photo-realistic images.
  • the inventive method processes a collection of objects represented by polygons in a computer into a hierarchy of bounding volumes, from a root volume bounding all objects to sub-volumes bounding individual polygons or a small collection of polygons. Many details in the process of generating bounding volume hierarchies can be automated with the present invention and do not require user intervention.
  • the basic principle employed in this invention uses clues from simplified models to partition a given polygonal model of a complex environment into components, each with a tight bounding volume. Such partitioning can be viewed as a recognition of the shape of the input model, whose essence is captured well by a simplified model.
  • the overall construction has the unique flavor of bottom-up in that polygons of models are distributed into various components, followed by top-down in that polygons within a component are partitioned recursively into smaller parts. This hybrid of top-down and bottom-up adapts itself very well to handle a diverse range of input models that some time favor top-down whereas at other times favor bottom-up.
  • bounding volume hierarchy The process of constructing bounding volume hierarchy is mostly automated, with minimal or no user intervention.
  • Some automatic simplification algorithm is first applied to an input model to derive different level-of-details simplified models. Then, the simplified models are used to derive components, sub-components of components and so on of the input model. Polygons within each sub-component (containing no other sub-component) are further subdivided recursively into small collections of polygons, each with an associated bounding volume. Results of the above can be linked up, in a natural way, into a required bounding volume hierarchy.
  • the framework includes the following steps:
  • Simplified Model Generation Various simplified models of an input model are generated.
  • the set of polygons, edges and points in a simplified model shows a sketch of the input model.
  • Each simplified model with polygons, edges and points, can be partitioned into parts that are to be used to guide the partition of the input model into components.
  • Component Tree Generation Components and sub-components generated above can be arranged into a tree (such as a binary tree in one embodiment) of component hierarchies, forming the highest levels of the eventual bounding volume hierarchy.
  • Bounding Volume Hierarchy Generation Each collection of polygons in each leaf of the component hierarchy is recursively partitioned into smaller collections of polygons and is connected to the component hierarchy into a resulting bounding volume hierarchy. Such bounding volume hierarchy is stored for subsequent use to assist collision detection in 3D interactive applications or ray-tracing processes.
  • FIG. 1 is a block diagram of an exemplary raster graphics systems
  • FIG. 2 is a block diagram of the raster graphics system of FIG. 1 that shows a memory for storing simplified models and bounding volume hierarchy;
  • FIG. 3 is a flowchart that depicts the steps involved in the method of the invention.
  • FIG. 4a is an example of a component tree constructed during the step of component tree generation in the framework
  • FIG. 4b is a binary component tree converted from the component tree of FIG. 4a during the step of component tree generation in the framework;
  • FIG. 4c is a final BV-tree constructed from the binary component tree of FIG. 4b during the step of bounding volume hierarchy generation in the framework;
  • FIG. 5 shows the parts extracted from an example simplified model during the step of component derivation in the preferred method.
  • FIG. 1 illustrates an exemplary raster graphics system, which includes a main (Host) central processing unit CPU 100 connected to a graphics subsystem
  • the Host processor 100 executes an application program and dispatches graphics tasks to the graphics subsystem 200.
  • the graphics subsystem 200 outputs to a display device 300 connected thereto.
  • the graphics subsystem 200 includes a pipeline of several components that perform operations to prepare geometric entities for display on a raster display device 300.
  • a model of the graphics subsystem is employed that contains the following functional units. It should be realized that this particular model is not to be construed in a limiting sense upon the practice of the invention.
  • a Geometric Processor unit 210 receives configurations and commands from the main CPU 100 to perform geometric and perspective transformations, exact clipping on primitives against screen (window) boundaries, as well as lighting computations.
  • the resulting graphics primitives e.g. points, lines, triangles, etc., are described in screen space (integral) coordinates.
  • a scan conversion (rasterization) unit 220 receives the graphics primitives from the geometric processor unit 210.
  • Scan converter unit 220 breaks down the graphics primitives into raster information, i.e. a description of display screen pixels that are covered by the graphics primitives.
  • a graphics buffer unit 230 receives, stores, and processes the pixels from the scan conversion unit 220.
  • the graphics buffer unit 230 may utilize conventional image buffers and a z-buffer to store this information.
  • a display driver 240 receives pixels from the graphics buffer unit 230 and transforms these pixels into information suitable for display on the output display device 300, typically a raster screen such as a cathode ray tube.
  • Fig. 2 is a simplified diagram of a graphics processing system according to the invention.
  • an input device 10 inputs graphics data to be processed by the invention.
  • the CPU 100 processes the input data from input devices 10 by executing an application program.
  • CPU 100 also dispatches graphics tasks to the graphics subsystem 200 connected thereto.
  • the output results may then be stored and/or displayed by display/storage devices 300.
  • This invention may also take the form of an article of manufacture. More specifically, the article of manufacture is a computer-usable medium, including a computer-readable program code embodied therein wherein the computer- readable code causes a computer to execute the inventive method.
  • a computer diskette 320 which may be inserted into storage device 310 in Figure 2 is an example of such a computer-usable medium.
  • the computer-readable program code stored therein is transferred into the CPU 100.
  • the CPU 100 may be instructed to perform the inventive methods disclosed herein.
  • models are described in polygonal boundary representations. Models with curved surfaces are in general tessellated, i.e. approximated with planar polygons, for graphic purposes and thus also benefit from the simplification technique of the invention.
  • polygons of models are simply triangles; otherwise, additional processing can be carried out to triangulate polygons into triangles or, alternatively, to provide minor modification to the invention to replace triangles with general polygons.
  • the general framework includes the following steps: (1) a simplified model generation step 400, (2) a component derivation step 410, (3) a component tree generation step 420, and (4) a bounding volume hierarchy generation step 430.
  • FIG. 3 is a flowchart that depicts the flow of these inventive steps.
  • the outputs of model simplification are used to guide the construction of a bounding volume hierarchy for the input model.
  • a bounding volume hierarchy a BV-tree.
  • the input model is first passed to a model simplification process to generate a first simplified model of the lowest level of detail.
  • This simplified model is usually drastically simplified from the input model.
  • a component of the original model is formed by collecting all the original polygons that simplify into the primitives in the part. These disjoint components form a partition of the original model. Note that a component is a subset of the original model's polygons.
  • the first-level components derived using the first simplified model in the above step can be further decomposed into sub-components in the same way by invoking the model simplification process again with higher level of detail than the first simplification.
  • the results of the subsequent simplifications are then used by the step of component derivation to derive the sub-components.
  • FIG. 4a shows an example of a component tree.
  • a component tree can be viewed as the topmost levels of a bounding volume hierarchy.
  • the degree (which is the maximum number of children over all the internal nodes of the component tree) of the BV-tree can be high. Since high degree may be harmful to the performance of collision detection, there is usually a need to convert the original tree to a low- degree tree.
  • FIG 4b shows a binary component tree converted from the original tree in FIG 4a.
  • FIG 4c shows a BV-tree constructed from the example component tree in FIG 4b.
  • the framework has a few advantages.
  • the information obtained from the simplified models can allow a BV-tree building process to better partition the original model into components that may be more tightly bounded by a pre- specified type of simple bounding volumes. Since the number of components is usually much smaller than the number of polygons in the input model, it is now affordable to use a more exhaustive bottom-up algorithm to perform the conversion of the component tree to one with a low specified degree. The above two factors allow more efficient computation of a BV-tree that is good in its topmost few levels.
  • simplification algorithms are suitable for mesh models, which consists of a network of polygons forming a single, continuous surface, while some are suitable for more general polygonal models (e.g. polyhedral models) where arbitrary topology is allowed.
  • mesh models which consists of a network of polygons forming a single, continuous surface
  • more general polygonal models e.g. polyhedral models
  • These algorithms form a spectrum, ranging from fast, simple approaches with moderate fidelity to slower, more sophisticated methods with superb fidelity.
  • the inventive simplification algorithm is based on vertex-clustering approach, as disclosed in US application Ser. No. 09/065,488 filed 24 April 1998, entitled “Multi-Resolution Graphic Representation Generated By Weight-Controlled Vertex Clustering For Interactive Visualization Applications” that is incorporated by reference above.
  • This simplification is one of the few that is capable of handling general class of polygonal models.
  • This simplification algorithm herein, will be referred to as the floating-cell simplification (FCS) algorithm.
  • FCS algorithm outputs simplified models that may contain triangles, edges and points. From the observations by the inventors, in many cases, the edges give the most important clues to the basic shape of the model.
  • An edge represents an elongated part in the model, and once the elongated part is identified, a good way to bound it is to use a bounding volume that can be oriented to fit along the length of the elongated part.
  • Oriented bounding boxes (OBBs) and oriented cylinders are examples of such suitable simple bounding volumes.
  • OBBs have been chosen [S. Gottschalk, M.C. Lin and D. Manocha, "OBBTree: A Hierarchical Structure for Rapid Interference Detection", Computer Graphics (SIGGRAPH '96 Proceedings), pp. 171-179, 1996).
  • the set of triangles, edges and points in a simplified model shows a sketch of the model. Its vertices are also more uniformly distributed as compared to the original model.
  • the success of the invention depends on simplification that produces drastically simplified models that show good sketches of the input model.
  • FCS requires an input parameter of clustering cell width to determine the resolution of the simplified model.
  • the frequency distribution of the lengths of the edges indicates locations with drastic changes in frequencies. Such locations are good lengths for clustering cell widths.
  • a simple algorithm can be designed to detect automatically a few of such locations to generate simplified models.
  • the invention uses outputs from the simplification step in the construction of a bounding volume hierarchy (termed BV-tree).
  • BV-tree a bounding volume hierarchy
  • the basic idea is to use clues from simplified models to partition a given polygonal model into components with tight bounding volumes.
  • T be the set of triangles of the input model M where ones desire to construct a BV-tree, called B(7).
  • Each node v of B(T) corresponds to a subset T v of T, with the root node being associated with the full set T.
  • Each internal node v of B(T) has two or more children in which their associated subsets form a partition of T v .
  • the maximum number of children for any internal node of B(7) is called the degree of B(T).
  • AABBs axis-aligned bounding boxes
  • T be the set of triangles in a polygonal model M.
  • each triangle of 7 is simplified to a point, an edge or remains as a (possibly different) triangle.
  • S be the set of triangles, edges, and points of a simplified model m of M. Notice that all elements in S are open sets, i.e., each triangle does not contain the three edges on its boundary, and each edge does not contain the two points at its ends.
  • S is partitioned into parts, and then the triangles in 7 are divided into components (with respect to m) so that t , t 2 belong to a same component if and only if F m (t ⁇ ) and F m (t 2 ) are in a same part of S.
  • a part of S contains elements that are maximally connected among themselves as discussed next.
  • S 3 , S 2 , S T respectively as the set of triangles, edges, and points in S.
  • S 3 , S 2 , Si are initialized, respectively, to the set of triangles, edges and points in S;
  • Step 2.1 Form parts due to triangles */
  • Step 2.2 Form parts due to stray edges */
  • FIG. 5 shows the parts extracted by the above algorithm from an example simplified model. Also, simple data structures are sufficient, in particular, on keeping information about the triangles incident to each vertex.
  • the algorithm runs in time linear to
  • the partition of S can be viewed as a shape of the input model.
  • a single application of the above algorithm divides 7 into various components. This can be recursively applied, each time with a simplified model of higher level of detail, to obtain sub-components of components and so on.
  • the invention restricts the view of tn'to only F m .(T c ).
  • step 410 makes each remaining vertex in S T a separate part. This can result in unnecessary many parts and thus many small components of the original model.
  • remaining vertices in step 410 if incident to some simplified edges or triangles, need not form a separate part.
  • triangles of original model that simplified to each such vertex can be distributed into components that derived from simplified edges or triangles incident by the vertex.
  • One possibility is to use one or more partitioning planes cutting through the location of the vertex to distribute original triangles or duplicate them into the respective components. In the case of duplication, a triangle is considered being cut into pieces lying in the space of the respective components.
  • the components identified from 7 can naturally be arranged into a component tree C(7), in which each node represents a component, and its children, if any, represent the sub-components.
  • the component tree C(7) corresponds to the topmost levels of the whole bounding volume hierarchy of 7, B(7).
  • some nodes in C(7) may have many children and thus contribute to the high degree of the component tree.
  • high degree in a BV-tree may be ineffective for the purpose of collision detection, a few ways, as described below, can be used to convert C(7) into a binary tree before making it the topmost few levels of B(7).
  • v' is treated as a new child in place of v, and v ; in the set of children to repeat the process until only one child remains, which is the node v. It is natural to pick a pair where the resulting bounding volume of v' is minimum (for collision detection purposes) or surface-area of v' is minimum (for ray-tracing purposes). Though such an approach requires searching of the smallest bounding volume, it remains efficient and effective as the number of children is normally small.
  • the generated bounding volume hierarchy data structure may be embodied within storage device 310. In this way a uniquely created data structure may take physical form within the storage device 310 and thereby configure the storage cells therein.
  • collision detection checking for example, can be performed as usual: starting from the root r of the tree, to determine whether b(r) collides with the obstacle s (which can be another bounding volume) in question. If yes, explore children of r, with possibly the children of the obstacle s, and recurse.
  • B(7) in the current invention has the effect of promoting triangles in that each part can be reached efficiently without involving other parts.
  • the level of a triangle in B(7) is, thus, mainly dependent on the number of triangles to which the component belongs. In other words, triangles of the input model are no longer treated equally.
  • a balanced B(7) such as one created using spatial decomposition schemes, may result in a large total bounding volume and is thus not efficient for collision detection.
  • the method of the current invention is similar to the way one should construct a bounding volume hierarchy for many individual items in a room by treating each item with a bounding volume rather than taking the whole room to partition recursively.

Abstract

L'invention intègre la simplification de modèle et la hiérarchie de volume englobant pour les besoins de la détection des collisions dans les applications graphiques interactives en trois dimensions. Particulièrement, l'invention fournit un cadre général et propose, en mode de réalisation préféré, un procédé relatif à l'élaboration d'une hiérarchie de volume englobant qui repose sur les résultats de la simplification de modèle. Non seulement les modèles simplifiés sont utiles pour le rendu à résolutions multiples, mais encore ils peuvent fournir des indices quant à la forme des objets d'entrée. Ces indices contribuent à la dissociation du modèle d'objet en composantes qu'il est plus facile d'englober de manière serrée dans des volumes englobants de configuration simple. Le cadre et le procédé considérés reposent naturellement sur les approches ascendante et descendante de l'élaboration des hiérarchies, offrant ainsi les avantages des deux approches. Les étapes inhérentes à ce cadre et à ce procédé sont les suivantes : établissement de modèles simplifiés, élaboration de composantes à partir de ces modèles, établissement d'arborescence de composante, et établissement de hiérarchie de volume englobant. En réponse aux commandes de l'utilisateur, on effectue des opérations de calcul interactives, on procède à l'affichage et à l'enregistrement des modèles simplifiés et de la hiérarchie de volume englobant. Il est possible d'accomplir efficacement le traçage de rayon et la détection de collision en utilisant la hiérarchie de volume englobant établie aux fins de l'invention.
PCT/SG1999/000078 1998-07-18 1999-07-16 Systeme et procede permettant de creer des hierarchies de volume englobant par le biais de la simplification de modele WO2000004433A2 (fr)

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SG9903366A SG80633A1 (en) 1998-07-18 1999-07-14 System and method for creating bounding volume hierarchies utilizing model simplification
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EP1804183A1 (fr) * 2005-12-30 2007-07-04 Dassault Systèmes Procédé de sélection d'objets dans une base de données PLM et appareil mettant en oeuvre ce procédé
WO2007112486A1 (fr) * 2006-03-30 2007-10-11 Monash University Méthode de modélisation de l'interaction entre des objets déformables
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Cited By (7)

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Publication number Priority date Publication date Assignee Title
WO2003046772A3 (fr) * 2001-11-22 2004-02-26 Koenig & Bauer Ag Methode de conception et systeme cao
EP1605379A1 (fr) * 2001-11-22 2005-12-14 Koenig & Bauer Aktiengesellschaft Procédé et system CAD pour le dessin des ensembles
EP1804183A1 (fr) * 2005-12-30 2007-07-04 Dassault Systèmes Procédé de sélection d'objets dans une base de données PLM et appareil mettant en oeuvre ce procédé
US7620638B2 (en) 2005-12-30 2009-11-17 Dassault Systemes Process for selecting an object in a PLM database and apparatus implementing this process
US8013854B2 (en) 2005-12-30 2011-09-06 Dassault Systemes Process for displaying objects of a PLM database and apparatus implementing this process
US9135372B2 (en) 2005-12-30 2015-09-15 Dassault Systemes Process for selecting objects in a PLM database and apparatus implementing this process
WO2007112486A1 (fr) * 2006-03-30 2007-10-11 Monash University Méthode de modélisation de l'interaction entre des objets déformables

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