A Marching Method for Computing Intersection Curves of Two Subdivision Solids
نویسندگان
چکیده
This paper presents a marching method for computing intersection curves between two solids represented by subdivision surfaces of Catmull-Clark or Loop type. It can be used in trimming and boolean operations for subdivision surfaces. The main idea is to apply a marching method with geometric interpretation to trace the intersection curves. We first determine all intersecting regions, then find pairs of initial intersection points, and trace the intersection curves from the initial intersection points. Various examples are given to demonstrate the robustness and efficiency of our algorithm.
منابع مشابه
Algebraic pruning: a fast technique for curve and surface intersection
Computing the intersection of parametric and algebraic curves and surfaces is a fun damental problem in computer graphics and geometric modeling This problem has been extensively studied in the literature and di erent techniques based on subdivision interval analysis and algebraic formulation are known For low degree curves and surfaces algebraic methods are considered to be the fastest whereas...
متن کاملExtraction of Intersection curves from Iso-surfaces on co-located 3D grids
This paper presents new methods for efficient extraction of intersection curves between iso-surfaces of any pair of co-located 3D scalar fields. The first method is based on the Marching Cubes algorithm which has been enhanced to produce an additional data structure that makes it possible to reduce the complexity of the general surface intersection extraction from O(N) to O( √ N), where N denot...
متن کاملDescribing subdivision schemes with Lindenmayer systems
The continuous study related to subdivision schemes for curves, surfaces and solids borders on many interesting disciplines. One of these areas is the concept of Lindenmayer systems, which appears to be a well suited method to describe subdivision schemes. Unfortunately, only a few papers combining these two topics have been published. In this report we attempt to provide a clear overview of th...
متن کاملOther marching direction of third order
The main motivation of this work is the problem of compute intersection curve between two surface. The surface/surface intersection, is a fundamental problem in computational geometry and geometric modelling of complex shapes. In general surface intersections, the most commonly used methods include subdivision and marching. Marching-based algorithms begin by finding a starting point on the inte...
متن کاملEstimating Error Bounds for Ternary Subdivision Curves / Surfaces
We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after k-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametriza...
متن کامل