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Angular motion and CCD

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I been researching how to handle angular motion in Continuous collision detection and was wondering when only dealing with circle-circle collisions if there are any other ways besides using Conservative Advancement (from thread http://www.gamedev.net/community/forums/topic.asp?topic_id=556189). Without angular motion I have the following algorithm for finding Time of Impact:
    double testBallCollision(Ball b, double t) {
        if (t == 0.0) {
            return -1;
        // Calculate the movement vector a for t
        Vector movea = current.velocity * t;
        // Calculate the movement vector b for t
        Vector moveb = b.current.velocity * t;		
        double deltaX = b.current.position.x - current.position.x;
        double deltaXSquared = deltaX * deltaX;
        double deltaY = b.current.position.y - current.position.y;
        double deltaYSquared = deltaY * deltaY;
        int sumRadii = radius + b.radius;
        int sumRadiiSquared = sumRadii * sumRadii;
        double distSquared = deltaXSquared + deltaYSquared;
        // Reduce dynamic-dynamic collision to dynamic-static
        Vector movec = movea - moveb;
        // If the length of the movement vector is less
        // then the distance between the objects,
        // then there is no way they can hit
        if (movec.length() < sqrt(distSquared) - sumRadii) {
            return -1; // no collision
        Vector N = movec.normalize();        
        // Find C, the vector from the center of the moving
        // ball A to the center of ball B
        Vector C = b.current.position - current.position;
        // D is the point along movec that is closest to ball b
        // D = N . C = ||C|| * cos(angle between N and C)
        double D = N.dot(C);
        // Find the lenght of the vector C
        double lengthC = C.length();
        // sqrt(F) is the distance between the center of ball b
        // ad the closest point on movec
        double F = (lengthC * lengthC) - (D * D);
        // If the closest that A will get to B
        // is more than the sum of their radii, there's no
        // way they are going collide
        if (F >= sumRadiiSquared) {
            return -1; // no collision
        // We now have F and sumRadii, two sides of a right triangle.
        // Use these to find the third side, sqrt(T)
        double T = sumRadiiSquared - F;
        // If there is no such right triangle with sides length of
        // sumRadii and sqrt(f), T will probably be less than 0.
        // Better to check now than perform a square root of a negative number
        if (T < 0) {
            return -1; // no collision;
        // Therefore the distance the circle has to travel along the
        // movement vector is D - sqrt(T)
        double distance = D - sqrt(T);
        // Get the magnitude of the movement vector
        double mag = movec.length();
        // Finally, make sure that the distance A has to move
        // to touch B is not greater than the magnitude of the
        // movement vector.
        if (mag < distance) {
            return -1; // no collision
        // Return the time it takes ball A to travel this distance
        double collision_t = (distance / mag) * t;
        if (collision_t < 0.0 || collision_t > t) {
            return -1; // no collision

        return collision_t;

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I could be misunderstanding the question, but the angular momentum of circles won't affect the time of collision. At least as long as they have constant density. When a circle rotates around its center the space that it takes up doesn't change.

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The spin will make the ball curve when on the cloth of pool table. Which is what I'm trying to simulate, and so the path of the ball is not straight. So I was wondering if you can determine the Time of Impact when the path of the circle is not straight without using Conservative Advancement.

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