Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
The synthesis of solids bounded by many faces
Communications of the ACM
A system for sculpting 3-D data
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
A scan line algorithm for computer display of curved surfaces
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
A fast scan-line algorithm for rendering parametric surfaces
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
Efficient computation and data structures for graphics.
Efficient computation and data structures for graphics.
Computer display of curved surfaces.
Computer display of curved surfaces.
Piecewise-circular curves for geometric modeling
IBM Journal of Research and Development
Accurate triangulations of deformed, intersecting surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Boundary evaluation of non-convex primitives to produce parametric trimmed surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Accurate Solid Modeling Using Polyhedral Approximations
IEEE Computer Graphics and Applications
A surface intersection algorithm based on loop detection
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Hierarchical Data Structures and Algorithms for Computer Graphics
IEEE Computer Graphics and Applications
Boundary Evaluation Using Inner and Outer Sets: the ISOS Method
IEEE Computer Graphics and Applications
A Pyramidal Data Structure for Triangle-Based Surface Description
IEEE Computer Graphics and Applications
Computational Methods for Geometric Processing. Applications to Industry
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
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There are several successful systems that provide algorithms that allow for the intersection of polygonal objects or other primitive shapes to create more complex objects. Our intent is to provide similar algorithms for intersecting surface patches. There have been contributions to this concept at the display algorithm level, that is, computing the intersection at the time the frame is generated. In an animation environment, however, it becomes important to incorporate the intersection in the data generation routines, in order that those parts of the intersected object that never contribute to an image are not processed by the display algorithm. This only increases the complexity of the object unnecessarily, and subsequently puts an additional burden on the display algorithms. An algorithm is described which uses a modified Catmull recursive subdivision scheme to find the space curve which is the intersection of two bicubic patches. An associated data structure is discussed which incorporates this curve of intersection in the patch description in a way suitable for efficient display of the intersected object. Sample output of these intersections are shown which serve to illustrate the capabilities and limitations of the described procedures.