沿向量方向旋转矩阵？

Question

I have a player in the shape of a sphere that can move around freely in the directions x and z. The players current speed is stored in a vector that is added to the players position on every frame:

m_position += m_speed;

I also have a rotation matrix that I'd like to rotate in the direction that the player's moving in (imagine how a ball would rotate if it rolled on the floor). Here's a short video to help visualise the problem: http://imgur.com/YrTG2al

Notice in the video when I start moving up and down (Z) as opposed to left and right (X) the rotation axis no longer matches the player's movement.

Code used to produce the results:

glm::vec3 UP = glm::vec3(0, 1, 0);
float rollSpeed = fabs(m_Speed.x + m_Speed.z);
if (rollSpeed > 0.0f) {
    m_RotationMatrix = glm::rotate(m_RotationMatrix, rollSpeed, glm::cross(UP, glm::normalize(m_Speed)));
}

Thankful for help

Answer 1

Your rollSpeed computation is wrong -- eg, if the signs of m_Speed.x and m_Speed.z speed are different, they will subtract . You need to use the norm of the speed in the plane:

float rollSpeed = sqrt(m_Speed.x * m_Speed.x + m_Speed.y * m_Speed.y);

To be more general about it, you can re-use your cross product instead. That way, your math is less likely to get out of sync -- something like:

glm::vec3 rollAxis = glm::cross(UP, m_speed);
float rollSpeed = glm::length(rollAxis);
m_RotationMatrix = glm::rotate(m_RotationMatrix, rollSpeed, rollAxis);

Answer 2

rollSpeed should be the size of the speed vector.

float rollSpeed = glm::length(m_Speed);

The matrix transform expects an angle. The angle of rotation will depend on the size of your ball. But say it's radius r then the angle (in radians) you need is

angle = rollSpeed/r;

Answer 3

If I understood correctly you need a matrix rotation which would work in any axis direction(x,y,z).

I think you should write a rotate() method per axis (x, y, z), also you should point to direction on which axis your direction points, you should write direction.x or direction.y or direction.z and rotation matrix will understand to where the direction vector is being point.