Deformation of n-dimensional objects
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Direct manipulation of free-form deformations
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Dynamic deformation of solid primitives with constraints
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Geometric manipulation of tensor product surfaces
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
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
Relaxed parametric design with probabilistic constraints
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Simple constrained deformations for geometric modeling and interactive design
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Direct manipulation techniques for 3D objects using 2D locator devices
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Geometric modeling: a new fundamental framework and its practical implications
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Volume-preserving free-form solid
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Techniques for interactive design using the PDE method
ACM Transactions on Graphics (TOG)
Volume-Preserving Free-Form Solids
IEEE Transactions on Visualization and Computer Graphics
| Hi-index | 0.00 |
Point displacement constraints constitute an attractive technique for interactive design of smooth curves, surfaces, and volumes. The user defines an arbitrary number of “control points” on the object and specifies their desired spatial location, while the system computes the object's degrees of freedom so that the constraints are satisfied. A constraint-based interface gives a feeling of direct manipulation of the object. In this article we introduce soft constraints, constraints which do not have to be met exactly. The softness of each constraint serves as a nonisotropic, local shape parameter enabling the user to explore the space of objects conforming to the constraints. Additionally, there is a global shape parameter which determines the amount of similarity of the designed object to a rest shape, or equivalently, the rigidity of the rest shape.We present an algorithm termed probabilistic point constraints (PPC) for implementing soft constraints. The PPC algorithm views constraints as stochastic measurements of the state of a static system. The softness of a constraint is derived from the covariance of the “measurement.” The resulting system of probabilistic equations is solved using the Kalman filter, a powerful estimation tool in the theory of stochastic systems. We also describe a user interface using direct-manipulation devices for specifying and visualizing covariances in 2D and 3D.The algorithm is suitable for any object represented as a parametric blend of control points, including most spline representations. The covariance of a constraint provides a continuous transition from exact interpolation to controlled approximation of the constraint. The algorithm involves only linear operations and allows real-time interactive direct manipulation of curves and surfaces on current workstations.