The trick is realizing that a collision only occurs if these two positions have different locations in relation to the plane - if they're both in front of or both behind the plane, no collision occurred and we can return from the function. Since we're only concerned with detecting collisions for moving objects, there must be a start position where the object moved from (p start) and a destination position (p dest) to which the object is moved. And of course we know that if p = 0 the point lies on the plane. If p > 0, the point is in front of the plane. Now that we've determined the collision surface's normal vector and distance from the origin (A, B, C, and D) we can use the Plane Equation for something really cool: determining if a given point lies on the plane! When we plug a point P=(x,y,z) into the left side of our revised plane equation DotProduct(N, P) + D we get a result value, p. Finally, the normal vector is normalized (made to have a length of 1.0) to simplify calculations.Ĭlassify the start and destination points. We compute the normal vector by generating a vector from vP1 to vP2 and another from vP2 to vP3 and then take the cross product of those two vectors to obtain the normal vector. The simplest 2D plane we can create in 3D space is a triangle with three vertices (call them vP1, vP2, and vP3) and I will focus on a triangular collision surface for simplicity. A normal vector is computed by taking the cross product of two vectors on the plane. Get the collision surface's normal vector.Īs noted above, in order to detect if a point is on our collision surface (such as a wall we want to prevent the player from running through), we need to know the normal vector perpendicular to the surface. Also note that since the dot product of vectors (A,B,C) and (x,y,z) equals Ax + By + Cz, we can rewrite the Plane Equation as DotProduct(N, P) + D = 0 for N=(A,B,C) and P=(x,y,z). If we plug in A, B, C, D, x, y, z and get any value other than zero, the point (x,y,z) is not on the plane. The plane equation tells us that a point (x,y,z) is on a plane having normal vector (A,B,C) and distance D from the origin when Ax + By + Cz + D = 0. Understand the Plane Equation: Ax + By + Cz + D = 0 Here's a description of the code, broken into seven steps to help you understand this basic form of collision detection. It works well enough in my Sk圜op demo because all I need to check is if the tip of the primary ship intersects the surface of other ships. In my previous post I presented a function for detecting collision of a point in 3D space with a plane (surface of an object).
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