Collision Response: game character vs. density function

Question

Introduction

I am working on my own "novelty" game-engine project, where the world is represented by a continuous density function. It has only one interface, a function that returns the density at a given point:

float sample(float x,float y,float z);

I triangulate this density into an iso-surface for density == 1.0 using marching cubes. The iso-surface is then rendered using OpenGL to display the result on screen.

I have made a function using newton's method to approximate the nearest point in the volume with density equal to 1 (within an error margin) for a certain direction, like this:

vec3d hitTest(vec3d &origin, vec3d &direction);

I can use this to perform collision detection between my main character and the volume, by seeing if the character has transitioned from "outside" to "inside" of the volume during update. I am also able to find the normal at the hit point by doing 3 hit-tests and doing some simple vector math "(a-b).crossProduct(a-c)" or some such.

Question

How would I be able to calculate the proper collision response?

I am no expert in collision detection/response, so what I am after is a clear and consise explanation of what makes a "physically correct" impulse collision under my foretold circumstances.

Source code in pseudo/C++ is a big bonus!

Thanks!

Answer 1

Common physics engines only need collisions defined by:

• the position of the point of contact
• the surface normal
• the position/velocity of the moving body (managed b the engine itself)

Therefore, you should be able to use a stock physics engine, as long as it supports plugging in custom collision shapes. I recommend doing so, as it gets you a lot of flexibility to add more interesting physics.