正确定向3D网格以指向其前进方向

Question

I'm trying to get a mesh to traverse a circuit across a sphere. I took the image that is wrapped around the sphere, and coloured the path that I want the mesh to follow. Then I computed all of the (u, v) points of the path. Using the (u, v) points, I convert to spherical coordinates to get the mesh onto the sphere, and set the rotations around the X and Y axes rot.x and rot.y , so that the mesh is tangent to the sphere and faces the north pole of the sphere. My problem is getting the mesh to face the direction it's heading in. The third rotation variable, rot.z , is used to set the heading of the mesh. Currently, I get the (u, v) points from the 5th to 14th points to come, and take the average of the angles of elevation of the line segment of the current point and each of the 10 future points. This works, but the two drawbacks are that the heading vibrates very frequently, and also the heading has a tendency to be inaccurate when turning somewhat sharply. What is a good method for calculating the heading of the mesh?

Answer 1

An easy approach is to build a rotation matrix. With that you don't have to think about angles, because if you know the direction and either the up or right vector all entries can be calculated. In your case the direction is the tangent on the sphere and the up vector the normal at that point.

vec3 direction = tangent;
vec3 up = normal;
vec3 right = cross(direction,up);

mat3 m;
m[0] = right;
m[1] = up;
m[2] = direction;