Classifications

• • 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

Definitions

• the present invention relates generally to computer graphics and solid modeling, and more particularly, to methods and apparatuses for representing and displaying an object of its skeleton, atomic parts, and hierarchy.
• a polygon mesh is inherently unstructured, making it expensive to perform geometric operations such as intersection tests in collision detection and ray tracing.
• the object hierarchy is most natural in terms of the human concept of shape. This has to do with the fact that cognition works best for hierarchically organized systems.
• the present invention describes an algorithm for determining first a collection of atomic parts of an input polygon mesh and for determining a unique hierarchy from the atomic parts. It is conceivably easy to obtain an object hierarchy from certain representations of models, for instance, constructive solid geometry models. However, the same cannot be said of geometric models, particularly B-rep models, which are by far the most prevalent.
• UCOLLIDE [TAN99] is a collision detection system that makes use of simplification to compute bounding volume hierarchies.
• bounding volume hierarchies are generated by top-down partitioning or bottom-up merging. Bottom-up methods only work well for organizing objects in a scene, and not polygons per se. Top-down methods perform poorly when the object to be partitioned consists of many sparsely arranged parts. Hence, we can conclude that it is hard to achieve optimal or near optimal bounding volume hierarchies using either method.
• [TAN99] takes a radically different approach. Using simplification and shape analysis, the major components of an object can be extracted. Further shape analysis on the simplified model yields the components of the model. Partitioning on each component can then be done using traditional top-down methods. It is easy to see why this method is superior to previous ones like [GOTT96]. Firstly, the sum of bounding volumes in [TAN99] is smaller, due to more intelligent partitioning. Since the nodes of the hierarchy are organized by components, it is also easier to zoom into a particular region during intersection tests.
• LOD level-of-details
• simplification using vertex clustering is not incremental.
• the algorithm needs to be invoked a number of times for LOD generation and this can cause a performance penalty.
• an alternative formulation of shape extraction is developed.
• the invention described herein satisfies the above-identified needs and overcomes the limitations of the prior invention by [TAN99].
• the present invention describes a new system and method to effectively generate object hierarchies, for purposes of various interactive applications such as: (i) organize an arbitrary mesh for scene management and view-dependent simplification;
• a method for execution by a data processor that generates effective object hierarchies.
• the method includes the following steps: (1 ) Preprocessing. This is to prepare data structures for subsequent processes. (2) Skeletonization. This is the process of deriving a skeleton of the input model, where skeleton is a fully collapsed body of the model. (3) Generating Atomic Parts. This is the process of obtaining various features (which is a part of the model that is distinctively autonomous from its connected or neighboring body) from the skeleton. (4) Postprocessing. This process connects various atomic parts obtained into a hierarchy.
• FIG. 1 is a block diagram of an exemplary raster graphics systems
• FIG. 2 is a simplified diagram of a graphics processing system according to the invention
• FIG. 3 is a flowchart that depicts the steps of the method of the invention.
• FIG. 4 is an edge contraction example utilizing method as described in the invention.
• FIG. 5 is a flowchart that depicts the operation of the method of the invention.
• FIG. 1 illustrates an exemplary raster graphics system that includes a main (Host) processor unit 100 and a graphics subsystem 200.
• 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/.storage device 300 connected thereto.
• the graphics subsystem 200 includes a pipeline of several components that perform operations necessary to prepare geometric entities for display on a raster display/storage 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 performs 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 unit 240 receives pixels from the Graphics Buffer unit 230 and transforms these pixels into information displayed on the output display device 300, typically a raster screen.
• 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.
• FIG. 3 shows a dataflow representation of the algorithm.
• preprocessing is to compute the necessary data structures required for subsequent processing.
• steps are performed: (P1 ) making a copy of the original tessellated triangle list, (P2) computing vertex neighborhood graph, (P3) computing incident edge table, and (P4) computing min heap for all the edges in the model. Notice that some of these steps, such as (P2) and (P3), are not necessary if input object representation comes with such information.
• the original model is represented by a vertex table VT and a triangle list TL.
• the vertex table VT contains the supporting vertices used in the model.
• the triangle list TL contains the triangles used in the model and each triangle is represented as an ordered list of references (indices) to the vertex table VT.
• indices references to the vertex table VT.
• there may be other augmented structures such as facet normal table and vertex normal table, but these are normally not used.
• the contents of the vertex table VT and triangle list TL are volatile during the execution of the algorithm.
• the original model can be represented as an edge-based data structure (instead of vertex-based as assumed in the description) such as the winged-edge data structure and quad-edge data structure [GUIB85]. It is straightforward for those skilled in the art to do the necessary adaptation from the following description to work on edge-based data structures. (P1 ) Making a copy of the original tessellated triangle list
• the edge contraction step performs in-place updating on the triangle list as new vertices are added.
• the triangle list is used for rendering of intermediate results.
• the vertex neighborhood graph VNB is used extensively during the edge contraction step.
• a simple way of implementing VNB is to use a two-dimensional array where each row represents the list of vertices related to the vertex index.
• a more efficient method is to use an adjacency list.
• the incident edge table INC is another data structure used in edge contraction.
• the elements of the incident edge table INC are defined as follows: for any valid edge (vO, v1 ) in the model, INC(vO, v1 ) gives the list of triangles that are incident to this edge.
• the incident edge table INC is implemented using a hash table. A simple hashing formula could be given as follows:
• the min heap is a data structure whereby the smallest element or the element with the smallest weight is always at the top of the heap. Thus, it is easy to retrieve the smallest weight item from the min heap. It is also efficient to remove the smallest weight item whilst maintaining the property of the min heap.
• the min heap is then obtained by adding all edges using the length of each edge as its weight. Thus, edges are retrieved in increasing order of length.
• the weight of each edge is computed based on some pre-calculated value of its vertices.
• Simplification is the process of obtaining a simpler form of a model while preserving certain attributes, such as appearance, as much as possible.
• a simpler model is one with fewer numbers of triangles and vertices. While the applications of simplification are mainly in the arena of level-of-detail modeling, there have been ingenious applications like
• the process of skeletonization in this invention is different in its methodology of edge contraction. Furthermore, the resulting skeleton is not the end product; rather the crux of the operation lies in the association of triangles into parts forming the skeleton.
• a skeleton is defined as the result of a collapsed model.
• Edge contraction refers to the process of collapsing edges into vertex. For the purpose of describing the invention, assume that the current edge to be collapsed is represented by (v0,v1 ) where vO and v1 are the vertices of its endpoints. FIG. 4 illustrates this process. Unless otherwise stated, edge contraction is performed until the min heap MH of all edges is empty (SO). An additional data structure is required in this method to store associated triangles and this is known as the associated triangle list ATL (which is initialized to empty set at the beginning of the skeletonization step).
• the detailed steps in edge contraction consist of: (S1 ) creation of new vertex, (S2) updating of associated triangle list ATL, (S3) updating of incident edge table INC, (S4) updating of vertex neighborhood graph VNB, (S5) updating of triangle list TL, (S6) updating min heap MH and skeleton S.
• vO and v1 are vertices to be collapsed
• a straightforward method of creating a new vertex vn would be (v0+v1 )/2.
• this does not take into consideration the relationship of vO, v1 and the skeleton S.
• the new vertex is given the coordinate of vO or v1 if either vO or v1 belong to an existing edge in skeleton S.
• the new vertex vn is appended at the end of the vertex table VT.
• vO and v1 are vertices of at least one triangle
• the collapsing of vO and v1 would cause at least one triangle to be removed from the model.
• the change of vertex numbering i.e. vO -» vn and v1 ⁇ vn
• the purpose of this step is to keep track of the removed triangles, as well as to update the vertex number in the associated triangle list ATL.
• the collapsing operation (vO, v1) ⁇ vn requires that the incident edge table INC - lo be updated.
• the algorithm for performing this update is given as follows: (i) for each vertex v* in VNB(vO) ⁇ ⁇ v1 ⁇ , rename INC(vO, v * ) as INC(vn, v * ) (ii) for each vertex v * in VNB(v1 ) ⁇ ⁇ vO ⁇ , rename INC(v1 , v * ) as INC(vn, v * ) (iii) for each triangle T in INC(vO, v1 ) with v2 be its third vertex, do delete T from INC(v2, vn)
• step (S3) it is mandatory to maintain the validity of vertex neighborhood graph VNB after the collapsing operation.
• the algorithm for this update is as follows:
• VNB(vn) VNB(vO) VNB(v1 ) ⁇ ⁇ vO, v1 ⁇
• VNB(v * ) VNB(v * ) ⁇ ⁇ vO, v1 ⁇ ⁇ vn ⁇
• the triangle list TL is updated so that collapsed vertices are renamed to vn. Note that if a high fidelity rendering is required, the affected normals in facet normal table and vertex normal table are to be recomputed. For the sake of efficiency, the updating of min heap MH and skeleton S are also performed under this step. It is not efficient to update MH directly, as this would involve examining the entire heap. Instead, only affected edges are reinserted into the min heap MH. When an edge is retrieved, its validity can be ascertained by checking against the incident edge table INC.
• step G1 An atomic part is defined as the collection of triangles that represent a connected skeleton. It is obtained from the following derivation:
• R be a relation on S such that aRb (i.e. a related to b) if there exists a path from a to b in S.
• R is an equivalence relation under S.
• the objective of post-processing is to derive the object hierarchy representing the original model M by organizing the atomic parts in a meaningful way.
• the object hierarchy is defined as a rooted tree where the root node is the original model M and each level below it is a breakdown of the node into mutually exclusive parts.
• the leaf nodes are atomic parts obtained in previous step.
• connection graph G is also disjointed.
• each connected subgraph is treated as an independent connection graph and is dealt with separately. Spatial analysis (see [TAN99]) could later be applied to join them up into a hierarchy. For the rest of the discussion on hierarchy building, G is assumed connected.
• step T1 is to compute the minimal spanning tree (MST) G' of G.
• MST minimal spanning tree
• the cost of each edge in G could be the some function, such as cosine, of the angle formed by. orientations of the endpoints.
• the cost function is chosen as such because a sharp angle formed by the parts indicate that they probably should not be joined in the first place.
• orientation is approximated by the largest eigenvector in the principal component analysis (PCA) of the object.
• PCA principal component analysis
• step T2 hierarchy construction can begin (step T2).
• Three types of hierarchical construction method are disclosed in the following paragraphs: (1 ) unrooted folding method (2) rooted folding method (3) common edge method. The use of a particular method may depend on the eventual applications of the constructed hierarchy.
• This method applies to the default configuration, in which G' is unrooted. Nodes of degree n (n > 1 ) with at least (n - 1 ) leaf neighbors are tagged. At each step of the algorithm, tagged nodes are collapsed to form a new node in the object hierarchy H.
• the algorithm for building H is as follows: add P 1t P 2 , ..., P m to H while
• > 1 add nodes of degree n with at least ( ⁇ -1) leaf neighbors to a queue, Q while P dequeue(Q) is not empty create a new node M' in H to be parent of leaf neighbors of P create a new node M" in H to be parent of M' and P delete leaf neighbors of P from G' rename P to M" in G'
• the unrooted folding method gives a simple way of constructing the hierarchy, without a priori knowledge of the model.
• the hierarchy constructed this way may be lopsided and not really reflect the natural partitioning of the model.
• a better way would be to pick a representative node in G' to be the root.
• a representative node could be the node with the largest bounding volume (representing a dominant part), or one with the highest degree (representing a center of focus), or could be selected manually by the user.
• Hierarchy construction would be similar as before, except that it is now done bottom-up.
• the rooted folding method for building H is as follows: add P 1l P 2 , ..., P m io H while
• > 1 let h be the height of G' add nodes at level ( ⁇ -1) to Q while P dequeue(Q) is not empty create a new node M' in H to be parent of leafs of P create a new node M" in H to be parent of M' and P delete leafs of P from G' rename P to M" in G'
• the method of construction is to keep removing edges based on a function of its metric. Such function may either be taking, in one embodiment, the largest, or, in another embodiment, the smallest metric.
• the algorithm for building H is as follows: add P,, P 2 P m to H while I G' ⁇ > 1 get (P, P j ) from G'with f (relative(P t , P y )) where f could be max or min function create a new node M' in H to be the parent of P t and P, collapse P, and P, to new node M' (corresponding to M' in H ) in G'
• f could be max or min function
• UCOLLIDE [TAN99] uses a series of simplified models to extract parts of models, hence taking advantage of their shape. However, it is not clear how many simplified models to use or how to select them to get the best result.
• This invention presents an automated way of obtaining the object hierarchy that is easily convertible into a bounding volume hierarchy suitable for collision detection and ray tracing.
• the atomic parts P 1t P 2 , ... , P m which form the leaf nodes of H are in general simple shapes. Hence top-down partitioning methods can be applied effectively to reduce P ; - to leaf nodes containing a single or small number of triangles.
• the MST of each connected subgraph G forms a hierarchy /-,- representing the object hierarchy of congregate part R the collection of polygons of the nodes in G,.
• bounding_box(Ri) be the size of the bounding volume of PC,.
• the choice of bounding volumes is application dependent and transparent to the algorithm.
• the algorithm for merging the various H makes use of pair-wise merging of smallest enclosing bounding volume to obtain a locally optimal solution.
• the resulting tree H may be reorganized by picking a new root to achieve a more balanced result.
• H may also be converted into a binary tree. Note that this is done on a per node basis, and does not involve alteration to the original model M.
• FIG. 5 is a flowchart that depicts the operation of the method of the invention in obtaining object hierarchies.
• the system loads or generates a database of objects appearing in a scene (M1 ). These objects may be elements of, for example, a CAD database or a virtual environment.
• a scene M1
• skeleton, atomic parts, and object hierarchies are generated as detailed in FIG. 3.
• the input models and the skeletons, atomic parts, and object hierarchies are stored in the memory as shown in FIG. 2.
• the system is ready to begin an interactive display session with a user.
• User can issue commands to, for example, display skeleton, atomic parts, or object hierarchies.
• user can interactively do adjustment to modify skeletons, atomic parts or object hierarchies, and the system accesses the memory to obtain the suitable data structures for modification and to pass them to the graphics subsystem for display of the data structures on the display screen.
• the system can use skeletons, atomic parts, and object hierarchies to compute other data structures such as the bounding volume hierarchies, as described earlier, for use in ray-tracing or virtual environment navigation to determine collisions M5.

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