gl_transform.hh

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#ifndef GL_TRANSFORM_HH
#define GL_TRANSFORM_HH
 
// openGL ES 2.0 removed functions like
//   glRotate(), glTranslate(), glScale(), ...
// This code can be used to replace them.
//
// This code was inspired by the 'glm' library (though written from scratch).
// Compared to glm this code is much simpler but offers much less functionality.
//   http://glm.g-truc.net
 
#include "gl_mat.hh"
#include "gl_vec.hh"
 
namespace gl {
 
// Returns a 4x4 scaling matrix for the given xyz scale factors.
// Comparable to the glScale() function.
[[nodiscard]] constexpr mat4 scale(const vec3& xyz)
{
        return mat4(vec4(xyz, 1.0f));
}
 
// Multiplies the given matrix by a scaling matrix. Equivalent to (but more
// efficient than) 'A * scale(xyz)'.
[[nodiscard]] constexpr mat4 scale(const mat4& A, const vec3& xyz)
{
        return {A[0] * xyz.x,
                A[1] * xyz.y,
                A[2] * xyz.z,
                A[3]};
}
 
// Returns a 4x4 translation matrix for the given xyz translation vector.
// Comparable to the glTranslate() function.
[[nodiscard]] constexpr mat4 translate(const vec3& xyz)
{
        mat4 result;
        result[3] = vec4(xyz, 1.0f);
        return result;
}
 
// Multiplies the given matrix by a translation matrix. Equivalent to (but
// more efficient than) 'A * translate(xyz)'.
[[nodiscard]] constexpr mat4 translate(mat4& A, const vec3& xyz)
{
        return {A[0],
                A[1],
                A[2],
                A[0] * xyz.x + A[1] * xyz.y + A[2] * xyz.z + A[3]};
}
 
// Returns a 4x4 rotation matrix for rotation of the given 'angle' around the
// 'xyz' axis.
// Comparable to the glRotate() function, but with these differences:
//  - 'angle' is in radians instead of degrees
//  - 'axis' must be a normalized vector
[[nodiscard]] inline mat4 rotate(float angle, const vec3& axis)
{
        float s = sinf(angle);
        float c = cosf(angle);
        vec3 temp = (1.0f - c) * axis;
 
        return {vec4(axis.x * temp.x + c,
                     axis.y * temp.x + s * axis.z,
                     axis.z * temp.x - s * axis.y,
                     0.0f),
                vec4(axis.x * temp.y - s * axis.z,
                     axis.y * temp.y + c,
                     axis.z * temp.y + s * axis.x,
                     0.0f),
                vec4(axis.x * temp.z + s * axis.y,
                     axis.y * temp.z - s * axis.x,
                     axis.z * temp.z + c,
                     0.0f),
                vec4(0.0f,
                     0.0f,
                     0.0f,
                     1.0f)};
}
 
// Multiplies the given matrix by a rotation matrix. Equivalent to
// 'A * rotate(angle, axis)'.
[[nodiscard]] inline mat4 rotate(const mat4& A, float angle, const vec3& axis)
{
        // TODO this could be optimized (only a little), though it's rarely used
        return A * rotate(angle, axis);
}
 
// Returns a 4x4 rotation matrix for rotation around the X-axis. Much more
// efficient than calling the generic rotate() function with a vec3(1,0,0)
// axis.
[[nodiscard]] inline mat4 rotateX(float angle)
{
        float s = sinf(angle);
        float c = cosf(angle);
        return {vec4(1.0f, 0.0f, 0.0f, 0.0f),
                vec4(0.0f,  c  ,  s  , 0.0f),
                vec4(0.0f, -s  ,  c  , 0.0f),
                vec4(0.0f, 0.0f, 0.0f, 1.0f)};
}
 
// Multiplies the given matrix by a X-rotation matrix. Equivalent to (but more
// efficient than) 'A * rotateX(angle)'.
[[nodiscard]] inline mat4 rotateX(const mat4& A, float angle)
{
        float s = sinf(angle);
        float c = cosf(angle);
        return {A[0],
                A[1] * c + A[2] * s,
                A[2] * c - A[1] * s,
                A[3]};
}
 
// Returns a 4x4 rotation matrix for rotation around the Y-axis. Much more
// efficient than calling the generic rotate() function with a vec3(0,1,0)
// axis.
[[nodiscard]] inline mat4 rotateY(float angle)
{
        float s = sinf(angle);
        float c = cosf(angle);
        return {vec4( c  , 0.0f, -s  , 0.0f),
                vec4(0.0f, 1.0f, 0.0f, 0.0f),
                vec4( s  , 0.0f,  c  , 0.0f),
                vec4(0.0f, 0.0f, 0.0f, 1.0f)};
}
 
// Multiplies the given matrix by a Y-rotation matrix. Equivalent to (but more
// efficient than) 'A * rotateY(angle)'.
[[nodiscard]] inline mat4 rotateY(const mat4& A, float angle)
{
        float s = sinf(angle);
        float c = cosf(angle);
        return {A[0] * c - A[2] * s,
                A[1],
                A[2] * c + A[0] * s,
                A[3]};
}
 
// Returns a 4x4 rotation matrix for rotation around the Z-axis. Much more
// efficient than calling the generic rotate() function with a vec3(0,0,1)
// axis.
[[nodiscard]] inline mat4 rotateZ(float angle)
{
        float s = sinf(angle);
        float c = cosf(angle);
        return {vec4( c  ,  s  , 0.0f, 0.0f),
                vec4(-s  ,  c  , 0.0f, 0.0f),
                vec4(0.0f, 0.0f, 1.0f, 0.0f),
                vec4(0.0f, 0.0f, 0.0f, 1.0f)};
}
 
// Multiplies the given matrix by a Z-rotation matrix. Equivalent to (but more
// efficient than) 'A * rotateZ(angle)'.
[[nodiscard]] inline mat4 rotateZ(const mat4& A, float angle)
{
        float s = sinf(angle);
        float c = cosf(angle);
        return {A[0] * c + A[1] * s,
                A[1] * c - A[0] * s,
                A[2],
                A[3]};
}
 
// Note: Don't use "near" or "far" as names since those are macros on Windows.
 
// Returns a 4x4 orthographic projection matrix. Comparable to
// the glOrtho() function.
[[nodiscard]] constexpr mat4 ortho(
        float left,    float right,
        float bottom,  float top,
        float nearVal, float farVal)
{
        return {vec4(-2.0f / (left - right),  0.0f, 0.0f, 0.0f),
                vec4( 0.0f, -2.0f / (bottom - top), 0.0f, 0.0f),
                vec4( 0.0f,  0.0f,  2.0f / (nearVal - farVal),  0.0f),
                vec4((left    + right ) / (left    - right ),
                     (bottom  + top   ) / (bottom  - top   ),
                     (nearVal + farVal) / (nearVal - farVal),
                     1.0f)};
}
 
// Equivalent to calling the above ortho() function with:
//    ortho(0.0f, width, height, 0.0f, -1.0f, 1.0f)
// In other words setup an orthographic projection with "natural screen
// coordinates", (0,0) the top-right corner.
[[nodiscard]] constexpr mat4 ortho(float width, float height)
{
        return {vec4(2.0f / width, 0.0f, 0.0f, 0.0f),
                vec4(0.0f, -2.0f / height, 0.0f, 0.0f),
                vec4(0.0f, 0.0f, -1.0f, 0.0f),
                vec4(-1.0f, 1.0f, 0.0f, 1.0f)};
}
 
// Returns a 4x4 frustum projection matrix. Comparable to
// the glFrustum() function.
[[nodiscard]] constexpr mat4 frustum(
        float left,    float right,
        float bottom,  float top,
        float nearVal, float farVal)
{
        return {vec4((2.0f * nearVal) / (right - left), 0.0f, 0.0f, 0.0f),
                vec4(0.0f, (2.0f * nearVal) / (top - bottom), 0.0f, 0.0f),
                vec4((right   + left  ) / (right   - left  ),
                     (top     + bottom) / (top     - bottom),
                     (nearVal + farVal) / (nearVal - farVal),
                     -1.0f),
                vec4(0.0f,
                     0.0f,
                     (2.0f * farVal * nearVal) / (nearVal - farVal),
                     0.0f)};
}
 
} // namespace gl
 
#endif