Homework #2: Collision Detection Between Rigid Bodies Yi Hong

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1 Homework #2: Collision Detection Between Rigid Bodies Yi Hong 1. Problem A: Implementation Used source code for collision detection: vcollide o Collision detection among multiple objects. o Report the objects that are collided with each other. o Report the intersected polygons of the collided objects. Assumptions: o When an object has collisions with other objects, all components of its velocity will be flipped. o When an object has a collision with the cube, the confined region, this object will be reflected, that is, the component of its velocity that is orthogonal to the collided face of the cube will be flipped. Inputs for the sphere- like objects: o Random sizes o Random velocities o Each sphere will be triangularized. With changing the numbers of the latitude and longitude, the number of triangles for a sphere will be changed. Inputs for the cube: o 8 vertexes and 12 faces Fig.1: Two screen shots of simulated results. 2. Problem B: Analysis Environment for following analysis: Operate System: Mac OS X, version Processor: 2.5GHz Intel Core i5 Memory: 4GB 1600MHz DDR3 Graphics: Intel HD Graphics MB

2 Analysis part: Number of objects Number of Objects Time(s) Fig.2: Computation time when changing the number of objects. In this experiment, the number of the polygons for each object and the relative size of objects are kept unchanged, with 256 and 0.2 respectively. As we can see from Fig.2, when the number of the objects is increasing, the computation time for collision detections is increasing as well. That is, we need more time for collision detections because more objects will collide with each other. Complexity of objects Number of Polygons Time(s) Fig.3: Computation time when the number of polygons increases. In this experiment, the number of the objects and the relative size of each object are kept unchanged, with 20 and 0.2 respectively. Fig.3 shows that more polygons for each object will cost more time for computation. While compared with the increasing number of objects, the number of polygons has a smaller influence on the computation time because the cost part for the collision detection is when two objects are collided with each other and more objects will have larger probability that objects will collide.

3 Sizes of objects Relative Size of Objects Time(s) Fig.4: Computation time when the relative size of objects is changed. In this experiment, the number of the objects and the number of polygons are kept unchanged, with 20 and 256 respectively. From Fig.4, I found that when the objects were small, the computation time was less because fewer collisions were happened; however, when the objects became larger, the computation time was increased greatly, for example from 0.2 to This is reasonable because when the size for each object becomes larger, more collisions will happen among objects and between the object and the cube, so more computation time is needed to calculate the intersected polygons. 3. Problem C: Varying Parameters A simple prototype implementation o Coarse collision detection 1) Collision between the object and the cube: compute the distance of the object s center to the cube s faces and there will be a collision if the distance is less than the radius of the object. 2) Collision among the objects: compute the distance between two objects, if it is less than the sum of two objects radii, there may be collision. o Fine collision detection 1) When two objects, or the object and the cube, are detected to collide after the coarse collision detection, the next step is to use their polygon information to figure out which two polygons will be collided with each other. 2) The method for detecting triangle- triangle- intersection is from the article a fast triangle- triangle intersection test by Tomas Moller. Compare and contrast the performance o Number of objects In the first comparison, shown in Fig.5, the number of polygons is 256 and the relative size of the objects is 0.2, and only the number of the objects is increasing. o Number of polygon In the second comparison shown in Fig.6, the objects number is 20 and their relative size is 0.2, and only the number of the polygons for each object is increasing. o Relative size of objects

4 In the third comparison shown in Fig.7, the number of objects is 20 and the number of the polygons is 256, and only the relative size of the objects is increasing. As we can see from Fig.5 to Fig.7, the computation time of the simple collision detection method increases much faster than that of V- Collision for all three comparisons. We can conclude that V- Collision is more efficient than this simple collision. V- Collision Number of Objects Time(s) Fig.5: Comparison I between V- Collision and the simple collision detection. V- Collision Number of Polygons Time(s) Fig.6: Comparison II between V- Collision and the simple collision detection.

5 V- Collision Relative Size of Objects Time(s) Fig.7: Comparison III between V- Collision and the simple collision detection.