An adaptive subdivision method for surface-fitting from sampled data
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces
SIAM Journal on Numerical Analysis
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Polygonization of implicit surfaces
Computer Aided Geometric Design
Contour tracing by piecewise linear approximations
ACM Transactions on Graphics (TOG)
Adaptive generation of surfaces in volume data
The Visual Computer: International Journal of Computer Graphics
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
A fast triangle-triangle intersection test
Journal of Graphics Tools
A unified approach for hierarchical adaptive tesselation of surfaces
ACM Transactions on Graphics (TOG)
A locally parameterized continuation process
ACM Transactions on Mathematical Software (TOMS)
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
Curvature-Dependent Triangulation of Implicit Surfaces
IEEE Computer Graphics and Applications
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
On the exact computation of the topology of real algebraic curves
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
| Hi-index | 0.00 |
In computer graphics, most algorithms for sampling implicit surfaces use a 2-points numerical method. If the surface-describing function evaluates positive at the first point and negative at the second one, we can say that the surface is located somewhere between them. Surfaces detected this way are called sign-variant implicit surfaces. However, 2-points numerical methods may fail to detect and sample the surface because the functions of many implicit surfaces evaluate either positive or negative everywhere around them. These surfaces are here called sign-invariant implicit surfaces. In this paper, instead of using a 2-points numerical method, we use a 1-point numerical method to guarantee that our algorithm detects and samples both sign-variant and sign-invariant surface components or branches correctly. This algorithm follows a continuation approach to tessellate implicit surfaces, so that it applies symbolic factorization to decompose the function expression into symbolic components, sampling then each symbolic function component separately. This ensures that our algorithm detects, samples, and triangulates most components of implicit surfaces.