libLDMat

The fast, low level and non-bloated (maybe) math library.

This library is conformant with:

• x86-32:
  • CDECL
• x86-64:
  • System V AMD64 ABI (*nix systems)
  • Microsoft x64 calling convention (Windows)
• ARMv7-A:
  • Procedure Call Standard for the ARM Architecture

Algebra tutorial:

Data types:

The next datatypes are the ones currently handled by the library:

(Matrices are Row Major).

• SS: float. IEEE-754 single precision floating point number.
• DS: double . IEEE-754 double precision floating point number.
• ANGLE: A float. It stands for "angle in radians".
• V2: Vector 2. An array of two IEEE-754 single precision floating point numbers.
• V3: Vector 3. An array of three IEEE-754 single precision floating point numbers.
• V4: Vector 4. An array of four IEEE-754 single precision floating point numbers.
• QUAT: Quaternion. An array of four IEEE-754 single precision floating point numbers.
• UQUAT: Unitary Quaternion. The same as a Quaternion.
• EULER: EULER ANGLE. A Vector 3 plus a contiguous Scalar, tecnically a Vector 4 too.
• M2: Matrix 2, 2x2 Matrix. An array of four IEEE-754 single precision floating point numbers.
• M4: Matrix 4, 4x4 Matrix. An array of 16 IEEE-754 single precision floating point numbers.
• AM4: Affine transformation from Matrix 4. Is a Matrix 4, but only the upper 3x3 is used.

Operations:

• ADD: Addition.
• SUB: Substraction.
• MUL: Multiplication.
• DIV: Divition.
• DOT: Dot Product.
• CROSS: Cross Product.
• LERP: Linear Interpolation.
• NLERP: Normalized Linear Interpolation.
• NORM: Norm.
• NORMALIZE: Normalization.
• DISTANCE: Distance between two operands.
• INV: Invert an Operand.
• DIFF: Difference of two operands, not the same as a raw substraction.
• ANGLE: Calculate angle (in randians) of operand(s).
• xTOy: Convertion from x to y.
• ROT: Rotation.
• MAKE: Construct data.
• IDENTITY: It makes an identity matrix, it uses MAKE with a factor of 1.0.
• DET: Determinant.

Given an operation OP, and operand(s) of type x, then the operation is xOP, for example: M2MUL, which is a multiplicacion between two 2x2 Matrices. Given an operation OP and operands of different types, x and y, then the operation is xOPy, for example: M2MULV2, which is a multiplicacion between a 2x2 Matrix and a Vector 2.

Valid Operations:

• On SS: LERP.
• On DS: LERP.
• On V2: ADD, SUB, MUL, DIV, DOT, LERP, NORM, DISTANCE, CROSS, ANGLE.
  • By SS: MUL, DIV.
  • Special operations: V2V2ANGLE (Angle between two 2D points.)
• On V3: ADD, SUB, MUL, DIV, DOT, LERP, NORM, DISTANCE, CROSS.
  • By SS: MUL, DIV.
• On V4: ADD, SUB, MUL, DIV, DOT, LERP, NORM, DISTANCE.
  • By SS: MUL, DIV.
• On QUAT: MUL, NORMALIZE (TOUQUAT), TOM4.
  • On V3: ROT (QUATROTV3).
• On UQUAT: The same as QUAT's, INV, DIFF, NLERP.
• On M2: MAKE, IDENTITY, MUL, DET, INV, ADD, SUB.
  • On V2: MUL (M2MULV2).
  • By SS: MUL, DIV
• On M4: MAKE, IDENTITY, MUL, INV.
  • On V4: MUL
  • On V3: MUL
  • Special operations: AM4MULV3, PERSPECTIVE, ORTHO, LOOKAT.
• On EULER: TOQUAT.
• On ANGLE: RADTODEG, DEGTORAD, TOM2
  • On V2: ROT (ANGLEROTV2).

Usage:

Most binary operations uses this format:

void OPERATION(void * Destiny, void * SourceOperand1, void * SourceOperand2);

Most unary operations uses this format:

void OPERATION(void * Destiny, void * Source);

Scalar parameters are passed as value. Most scalar only operations uses this format:

float OPERATION(float Source);
double OPERATION(double Source);

For more complex operations refer to the respective definition files.

C/C++:

Example:

#include "LDMat/LDMat.h"
#include "stdio.h"

int main()
{
  float A[2] = {1,2};
  //The same as V2 A = {.x = 1, .y = 2};
  
  float B[2] = {3,4};
  //The same as V2 B = {.x = 3, .y = 4};
  
  float C[2];
  //The same as V3 C;
  
  V2ADD (C, A, B);
  //This could also be V2ADD(&C, &A, &B);
  //Because functions relies on pointers.
  
  printf("%f,%f\n",C[0], C[1]);
  //This could also be printf(%f,%f\n", C.x,C.y);
  
  return 1;
}

Geometry tutorial:

2D Data types:

• CIRCLE2: Vec3. Circle represented by a 2D point and a Radius.
• AABB2: Vec4. Generic Axis Aligned Bounding Box represented by two 2D points.
• TRI2: 3 Vec2. A triangle represented by an array of three 2D points.
• V2V2: Vec4. Generic composition of two 2D points, a line.
• RANGE2: Vec3. A cone made by two 2D points (a line) and a angle (radians).

3D Data types:

• SPHERE: Vec4. Sphere represented by a 3D point and a Radius.
• AABB3: 2 Vec3. Generic Axis Aligned Bounding Box represented by two 3D points.
• TRI3: 3 Vec3. A triangle represented by an array of three 3D points.
• V3V3: 2 Vec3. Generic composition of two 3D points, a line.
• RANGE3: 2 Vec3. A cone made by two 3D points (a line) and a angle (radians).
• PLANE: 2 Vec3. A plane represented by a point and a normal.

Common operations (there are a lot of variants):

• VS: Interception of two objects.
• CENTROID: Centroid of an Object.
• CLOSES: Closest object to another object.
• NORMAL: Calculation of normal vector.
• DISTANCE: Distance between two objects.

Modes:

Due to the many ways to represent these data types, the algoritms use flags to set the proper representation. (Refer to the header).