Collision Detection Of Composite Cone

Collision detection problem is a basic problem in computer simulation, CAD; robotics .It is mainly used to enhance the reality of virtual scene or applied for robot Path planning. Collision Detection algorithms are different for different applications, providing different information. Some applications require collision detection algorithm to give information of whether the collision occurred along their respective moving course of these two objects. Other applications require collision detection algorithm not only to give whether the collision occurred, but also to provide distance information: the shortest puncture distance between these two objects when there is a collision along their moving course and the minimum separation distance between these two objects when there is no collision.Currently, there are many collision detection methods. Usually, they are divided into two major categories: one is discrete collision detection, like algorithms based on computational geometry, based on separation plane, based on graphics hardware etc.; the other is continuous collision detection, such as swept volume algorithm based on duality and Minkowski Sum, and algebraic methods. Discrete Collision Detection Methods of two moving objects use time sampling. In each sampling time we judge whether the two static objects collide. In this kind of method, if the speed of moving objects is very high, or objects are very small, collision during inter zone of two sampling time may be missed. We can improve accuracy through shortening the time sampling interval, but this will reduce efficiency. Continuous Collision Detection methods constructed a continuous path. Based on the path between objects we judge whether these two objects collision. We studies continuous collision detection using algebraic methods.There are two algorithms in this article: one is collision detection of two moving composite cone using algebraic method, another is computing minimum distance of two moving composite cones.In algebraic method a collision condition using algebraic expression of two stationary objects is proposed, and then the movement of objects modeled as a function of time. Based on these former two factors, collision condition between two moving objects is proposed.Algebraic method can give information about collision position and collision time,but when the two object don't collide with each other,this method can't return the minimum distance and the time when they are closest.Computing minimum distance of two object is important for many applications,such as robotics, CAD/CAM, computer graphics.In robotic path design,distance information is need in force computing and compensate function.Distance information is important for collision detection and computer simulation. There are many algorithm to compute the distance of polyhedra,to a object with free surface we can also use this method using polyhedra simulate the object,but when the number of polyhedra using to simulating is large,it is difficult to use for realtime application.There are also some method direct detect two surface is collide or not,if so,the distance if zero.There are also some method computing the distance between surfaces,these method use such a geometry character:the direction of nomor on the closest point on two surface are colliner.These method can called geometry method,they all need to solve a equation or equations with a high degree.so they only suit to immobile objects.To moving object a sampling is needed,and this could be all right.This article we propose a method computing minimum distance of two moving compesite cone using algebraic method,we see the distance as a function of time,when the path of cone is determined,this method can return the minimum distance and the time when they are closest.Contents of this paper: use Rational movement as motion of objects in three dimensional space; calculated equations of motion through interpolation of the dynamic image control points of motion trajectory; propose collision detection of two composite cone under rational motion; propose collision detection algorithm of two moving composite cone using direct computation of curves; Bernstein polynomial form of the solution; distance formula is used in collision detection between two composite cone, which is formulated into three polynomials; Bernstein polynomial form of the solution;compute distance information: the shortest puncture distance between these two objects when there is a collision along their moving course and the minimum separation distance between these two objects when there is no collision.