Find angle (slope) of collision plane?

Question

I have implemented a collision and response system based on the famous "Improved Collision detection and Response" paper. However I'm having an issue with objects sliding backwards on slopes. I believe I could circumvent this issue if I understood how to find the angle of the plane of which my object is colliding with. Take the below screenshot as an example of the situation:

I know the following data:

• Position of player object (the ellipsoid at the bottom of the ramp)

• Vertices of the collision triangle

• Normal of the collision triangle
• Intersection point between player object and collision triangle
• Penetration distance between player object and collision triangle

How can I use this information to determine the angle of the collision triangle?

Answer 1

If you have the normal of the collision triangle, then you can do a dot product with a normal pointing up (0, 1, 0), the result will be related to the angle of the surface (0 when is completety vertical, 1 when it's completely flat, and in between)

That should be really all, you check that against a threshold to determine if you want the ellipsoid to slide or not.

I actually followed that same paper and this is how I implemented (my Up vector was 0,0,1)

// Check if the slide is too steep for gravity 
if (is_gravity) {
    var v1 = vector_normalize(velocity),
        v2 = [0, 0, 1 * sign(v1[2])],
        dp = dot(v1, v2);

    if (dp <= 0.70) {
        return true;
    } 
}