Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Loop detection in surface patch intersections
Computer Aided Geometric Design
Sweeping of three-dimensional objects
Computer-Aided Design
Visualization of swept hyperpatch solids
CG International '92 Proceedings of the 10th International Conference of the Computer Graphics Society on Visual computing : integrating computer graphics with computer vision: integrating computer graphics with computer vision
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Tangent, normal, and visibility cones on Be´zier surfaces
Computer Aided Geometric Design
Swept volume: a retrospective and prospective view
Neural, Parallel & Scientific Computations - computer aided geometric design
Analytical boundary of the workspace for general 3-DOF mechanisms
International Journal of Robotics Research
Multiresolution tetrahedral framework for visualizing regular volume data
VIS '97 Proceedings of the 8th conference on Visualization '97
Volume-Preserving Free-Form Solids
IEEE Transactions on Visualization and Computer Graphics
An Overview of Analytic Solid Modeling
IEEE Computer Graphics and Applications
A Hierarchy of Geometric Forms
IEEE Computer Graphics and Applications
Geometric Modeling for Swept Volume of Moving Solids
IEEE Computer Graphics and Applications
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Proceedings of the sixth ACM symposium on Solid modeling and applications
Interactive Direct Rendering of Trivariate B-Spline Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Preventing Self-Intersection under Free-Form Deformation
IEEE Transactions on Visualization and Computer Graphics
Fast swept volume approximation of complex polyhedral models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
VG '03 Proceedings of the 2003 Eurographics/IEEE TVCG Workshop on Volume graphics
Approximate swept volumes of NURBS surfaces or solids
Computer Aided Geometric Design
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The trivariate tensor-product B-spline solid is a direct extension of the B-spline patch and has been shown to be useful in the creation and visualization of free-form geometric solids. Visualizing these solid objects requires the determination of the boundary surface of the solid, which is a combination of parametric and implicit surfaces.This paper presents a method that determines the implicit boundary surface by examination of the Jacobian determinant of the defining B-spline function. Using an approximation to this determinant, the domain space is adaptively subdivided until a mesh can be determined such that the boundary surface is close to linear in the cells of the mesh. A variation of the marching cubes algorithm is then used to draw the surface. Interval approximation techniques are used to approximate the Jacobian determinant and to approximate the Jacobian determinant gradient for use in the adaptive subdivision methods. This technique can be used to create free-form solid objects, useful in geometric modeling applications.