gfx/maths3d.h
Three-dimensional vectors, 4x4 matrices, quaternions, and an arcball that turns mouse drags into a rotation.
#include <sonore/gfx/maths3d.h>- 4types
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Design notes
Why these live beside the OpenGL classes and not in geometry.h
geometry.h is the 2D world every widget is laid out in, and everything there is float because a knob at 63.5 pixels is a real position. These are the types a shader is FED: a model-view-projection matrix, a camera orbiting a spectrum waterfall, the orientation a user dragged a 3D scope into. Nothing in the 2D toolkit needs them, and nothing here needs a Component -- so they get a header of their own, with no platform code in it, and are usable (and tested) without a GL context at all.
The conventions, stated once
- Right-handed. A positive rotation about an axis turns counter-clockwise when the axis points at the viewer, which is what every GL tutorial, every textbook and every glm-style library assumes. Getting the hand wrong produces a scene that is mirrored, which does not read as a maths bug -- it reads as "the camera is behind the object".
- Matrix3D is COLUMN-MAJOR, mat[column * 4 + row], because that is the order glUniformMatrix4fv takes with transpose = GL_FALSE. A row-major store would need a transpose on every upload, or worse, would be uploaded untransposed and work until the first non-symmetric matrix.
- Products read right to left, as in the maths: (A * B) applied to v is A(B(v)), so
projection * view * modelis the usual spelling and a point goes through the model first. Transform in geometry.h names its compositionthenprecisely because left-to-right is the trap; here the operator is kept because a reader porting shader maths expects it.
- Quaternions are unit quaternions whenever they represent a rotation. fromAngle produces one; a product of two is one up to rounding, so anything that accumulates thousands of them -- an arcball does, once per mouse move -- renormalises as it goes. A quaternion that has drifted to length 1.01 rotates AND scales, and the object visibly grows.
Types 4
template <typename Type> class Vector3D
x, y and z, with the arithmetic a shader's inputs need.
template <typename Type> class Matrix3D
A 4x4 matrix, column-major, as OpenGL takes it.
Default-constructed it is the identity -- the one default for which "I forgot to set the model matrix" still draws something.
template <typename Type> class Quaternion
A rotation as a unit quaternion: the vector part and the scalar part.
Why not just matrices: interpolating two rotation matrices element by element produces something that is not a rotation at all -- the object shrinks through the middle of the move -- and composing thousands of them accumulates skew. A quaternion interpolates on the sphere (slerp) and renormalises with one division.
An arcball: mouse drags inside a rectangle turned into a rotation.
The rectangle is treated as the silhouette of a sphere. A point pressed on it is lifted onto the sphere's front surface, and dragging rotates the sphere so the point under the pointer STAYS under the pointer -- which is what makes it feel like grabbing an object rather than steering it. Outside the sphere's outline the point is held on the rim, so a drag around the edge spins about the view axis, the other thing a user expects to be able to do.
Coordinates are this SDK's: logical, y DOWN. The flip to the maths' y-up happens once, in the projection.