Primitive Geometric Operations on Planar Algebraic Curves with Gaussian Approximation

Primitive Geometric Operations on Planar Algebraic Curves with Gaussian Approximations

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 eecient algorithms for various primitive geometric operations, especially for those related with gradients such as common tangent...

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 Geometri Operations on Planar Algebrai Curves with Gaussian Approximation

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...

Geometric Modeling with Algebraic Surfaces

Research in geometric modeling is currently engaged in increasing the geometric coverage to allow modeling operations on arbitrary algebraic surfaces. Operations on models often include Boolean set operations (intersection, union), sweeps and convolutions, convex bull computa· tions, primitive decomposition, surface and volume mesh generatioD, calculation of surface area and volumetric properti...