stevesch-MathVec

Provides classes for

• vector2 : 2-element vector

• vector3 : 3-element vector

• vector4 : 4-element vector

• matrix4 : 4x4 matrix

• quat: quaternion

Typical operations for 3D rendering are provided for each of the above classes (transformation, projection, etc.).

Use in combination with stevesch-Mesh and stevesch-Display for rendering 3D objects on an SPI TFT screen.

Building and Running

Add library dependency, e.g.

lib_deps = 
  stevesch/stevesch-MathBase
  stevesch/stevesch-MathVec

Include in your code:

#include <stevesch-MathBase.h>
#include <stevesch-MathVec.h>

Example code:

using stevesch::vector3;
using stevesch::vector4;
using stevesch::matrix4;
using stevesch::quat;

Vector addition:

vector3 a(2.0f, 3.0f, 5.0f);
vector3 b(7.0f, 11.0f, 13.0f);
vector3 c;
c = a + b; // c == <9, 14, 18>; equivalent: vector3::add(c, a, b);

Vector transformation by a matrix:

vector3 a, b;
matrix4 m;
b = a.transform(m); // b = m*a

Vector transformation by a quaternion:

quat q;
vector3 axis(0.0f, 0.0f, 1.0f); // z axis (w ignored)
// already normalized in our case, but if not: axis.normalize();

// <axis> must be normalized for 'fromAxisAngle':
q.fromAxisAngle(axis, stevesch::degToRad(30.0f));

vector4 a(1.0f, 0.0f, 0.0f, 1.0f);
vector4 b;
q.rotate(b, a); // equivalent to b = m*a if q were converted to a matrix

Notes:

• Some vector operations are only implemented for vector4 (not vector3). When in doubt about the w-component of a vector4, set it to 1.0f.

• quaternions should almost always be normalized (q.abs() should be about 1.0) when using them as rotations. If you create them properly (e.g. using fromAxisAngle or fromMatrix), this will usually not be a big issue, but if you see that a quaternion is not normalized, something has probably gone wrong.