Primitive Geometric Operations on Planar Algebraic Curves with Gaussian Approximations

Gaussian Approximations of Objects Bounded by Algebraic Curves

We present a discrete approximation method for planar algebraic curves. This discrete approximation is hierarchical, curvature dependent, and provides eecient algorithms for various primitive geometric operations on algebraic curves. We consider applications on the curve intersections , the distance computations, and the common tangent and convolution computations. We implemented these approxim...

Primitive Geometric Operations on Planar Algebraic Curves with Gaussian Approximation

We present a curve approximation method which approximates each planar algebraic curve segment by discrete curve points at each of which the curve has its gradient from a set of uniformly distributed normals. This method, called Gaussian Approximation (GAP), provides efficient algorithms for various primitive geometric operations, especially for those related with gradients such as common tange...

Planar shape manipulation using approximate geometric primitives

We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is O(n log n + k) for an input of size n with k = O(n) consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms in flo...

Primitive Geometri Operations on Planar Algebrai Curves with Gaussian Approximation

Spline Approximations of Real Algebraic Surfaces

We use a combination of both symbolic and numerical techniques to construct several degree bounded G0 and G1 continuous, piecewise spline approximations of real implicit algebraic surfaces for both computer graphics and geometric modeling. These approximations are based upon an adaptive triangulation (a G0 planar approximation) of the real components of the algebraic surface, and include both s...