- In-depth documention is embedded in the header files
- You can find overview of the library in Getting Started section
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Vector Mathematics
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2D vectors
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3D Vectors
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4D Vectors
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Matrix Mathematics
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2x2 Matrix operations
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3x3 Matrix operations [WIP]
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4x4 Matrix operations
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Quaternion Mathematics
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Interpolations
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Rotations
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Conversion to euler angles [WIP]
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Euler angles to Quaternion [WIP]
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Complex Mathematics [WIP]
| Mathematical Type | Description | HPML Type |
|---|---|---|
| Vector 2D | a 2 dimensional vector | vec2_t |
| Vector 3D | a 3 dimensional vector | vec3_t |
| Vector 4D | a 4 dimensional vector | vec4_t |
| Quaternion | a quaternion | quat_t |
| Matrix 2x2 | a 2x2 square matrix | mat2_t |
| Matrix 3x3 | a 3x3 square matrix | mat3_t |
| Matrix 4x4 | a 4x4 square matrix, sizeof(mat4_t) != 64 bytes | mat4_t |
| Raw Matrix 4x4 | a 4x4 square matrix, sizeof(_mat4_t) == 64 bytes | _mat4_t |
| Complex Number | a complex number | complex_t |
2D Vectors
vec2_t v = { 1.0f, 2.0f }; // initializer
vec2_t position = vec2(1.3f, 4.5f); // constructor function
position = VEC2 { 4.5f, 3.2f }; // re-assigning th value
// constant vectors
vec2_t up = vec2_up(); // or vec2_down()
vec2_t left = vec2_left(); // or vec2_right()
vec2_t null_vector = vec2_null(); // or vec2_zero();
if(vec2_is_null(null_vector)) // checks if the vector is null
printf("Vector is null\n");
// adding & subtracting vectors
vec2_t final_position = vec2_add(2, position, vec2_down());
vec2_t another_position = vec2_sub(2, position, vec2_up());
// adding & subtracting more than 2 vectors at once
final_position = vec2_add(3, position, vec2_down(), vec2_left());
another_position = vec2_sub(3, position, vec2_down(), vec2_left());
// printing on the console window for debugging purpose
vec2_print(final_position); // final_position: (x, y)
vec2_print(another_position); // another_position: (x, y)
// interpolations [linear interpolation, and spherical linear interpolation]
vec2_t interpolated_vector = vec2_lerp(vec2(1.0f, 2.0f), vec2(4.0f, 5.0f), 0.2f);
vec2_t slerped_vector = vec2_slerp(vec2(1.0f, 2.0f), vec2(4.0f, 5.0f), 0.2f);
vec2_print(interpolated_vector);
vec2_print(slerped_vector);3D Vectors
vec3_t v = { 1.0f, 2.0f, 3.0f }; // initializer
vec3_t position = vec3(1.3f, 4.5f, 3.4f); // constructor function
position = VEC3 { 4.5f, 3.2f, 6.7f }; // re-assigning the value
// constant vectors
vec3_t up = vec3_up(); // or vec3_down()
vec3_t left = vec3_left(); // or vec3_right()
vec3_t null_vector = vec3_null(); // or vec3_zero()
if(vec3_is_null(null_vector))
printf("Vector is null\n"); // checks if the vector is null
// adding & subtracting vectors
vec3_t final_position = vec3_add(2, position, vec3_down());
vec3_t another_position = vec3_sub(2, position, vec2_up());
// adding & subtracting more than 2 vectors at once
final_position = vec3_add(3, position, vec3_down(), vec3_left());
another_position = vec3_sub(3, position, vec3_down(), vec3_left());
// printing on the console window for debugging purpose
vec3_print(final_position); // final_position: (x, y, z)
vec3_print(another_position); // another_position: (x, y, z)
// interpolations [linear interpolation, and spherical linear interpolation]
vec3_t interpolated_vector = vec3_lerp(vec2(1.0f, 2.0f, 5.0f), vec2(4.0f, 5.0f, 2.0f), 0.2f);
vec3_t slerped_vector = vec3_slerp(vec2(1.0f, 2.0f, 5.0f), vec2(4.0f, 5.0f, 2.0f), 0.2f);
vec3_print(interpolated_vector);
vec3_print(slerped_vector);2x2 Matrices
// initializer
mat2_t m = { 1.0f, 0.0f, 0.0f, 1.0f };
// matrix constructor of dimensions 2x2
mat2_t m1 = mat2(1.0f, 0.0f, 0.0f, 1.0f);
// identity matrix of dimensions 2x2
m = mat2_identity();
// trace calculation, i.e. sum of diagonal elements from left to right
float t = mat2_trace(m1);
// addition
mat2_t m2 = mat2_add(m, m1);
// multiply with scalar
mat2_t m3 = mat2_mul_with_scalar(m2, 5.0f)
// linear interpolation calculation for each elements of the matrices
mat2_t lp = mat2_lerp(m2, m3, 0.7f);
// calculates and returns approx 90 degree anticlockwise 2D rotation matrix
mat2_t rotation = mat2_rotation(1.57)
// calculates and returns inverse of a 2x2 matrix (non-singular matrix)
mat2_t opp_rot = mat2_inverse(rotation)
// print the elements of 2x2 matrix to stdout
mat2_print(opp_rot);4x4 Matrices
// initializer
mat4_t m =
{
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
// matrix constructor of dimensions 4x4
mat4_t m1 = mat4(1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f);
// identity matrix of dimensions 4x4
m = mat4_identity();
// copy contents of m1 matrix into m1 matrix
mat4_copy(m, m1);
// move identity matrix (r-value) into m matrix
mat4_move(m, mat4_identity());
// returns the last column (considered as position vector in a translation vector)
vec4_t position = mat4_get_position(m);
// returns the euler angles rotation along each axis in radians in a RTS matrix
vec4_t euler_angles = mat4_get_rotation(m);
// returns the diagonal elements from left to right
vec4_t scale = mat4_get_scale(m);
// calculates and returns determinant of 4x4 matrix
float det = mat4_det(m);
// multiply 2 4x4 matrices together, associates from right to left
mat4_t product = mat4_mul(2, m, m1);
// creates a scale matrix (a diagonal matrix) which scales x, y and z components by 2.0f
mat4_t scale_matrix = mat4_diagonal(2.0f, 2.0f, 2.0f, 1.0f);
// multiply 4x4 matrix by 2.0f (a scalar)
mat4_t t = mat4_mul_scalar(scale_matrix, 2.0f);
// multiplies each components of first matrix to the correponding components of second matrix
mat4_t t1 = mat4_mul_component_wise(scale_matrix, scale_matrix);
// transposes 4x4 matrix along the left-to-right diagonal
mat4_t trans = mat4_transpose(t1);
// linearly interpolates each components of the two matrices
mat4_t l = mat4_lerp(t1, t, 0.7f);
// calculates and returns inverse of 4x4 non-singular matrix, if the matrix is singular then throws an exception
mat4_t inv = mat4_inverse(l);
// prints the components of a 4x4 matrix on stdout
mat4_print(inv);NOTE: To convert mat4_t to raw _mat4_t: simply access the union member raw4x4f32 in mat4_t object.