Rotation identity

rotationIdentity.cpp

// why does makeTransform1 give the same results as makeTransform2?

mat3 rotationMatrix(float angle, vec3 axis) {
    ... // returns a 3x3 rotation matrix for rotating about the given axis
}


mat3 makeTransform1(float alpha, float beta, float gamma) {
    mat3 alphaTransform = rotationMatrix(alpha, vec3(0.0, 1.0, 0.0));
    mat3 betaTransform  = rotationMatrix(beta,  vec3(1.0, 0.0, 0.0));
    mat3 gammaTransform = rotationMatrix(gamma, vec3(0.0, 1.0, 0.0));
    return alphaTransform * betaTransform * gammaTransform;
}

mat3 makeTransform2(float alpha, float beta, float gamma) {
    mat3 alphaTransform = rotationMatrix(alpha,                                  vec3(0.0, 1.0, 0.0));
    mat3 betaTransform  = rotationMatrix(beta,                  alphaTransform * vec3(1.0, 0.0, 0.0));
    mat3 gammaTransform = rotationMatrix(gamma, betaTransform * alphaTransform * vec3(0.0, 1.0, 0.0));
    return gammaTransform * betaTransform * alphaTransform;  // NOTE: reversed order
}