Quaternion Library
This repository represent an interface (library) of Quaternions and the most common operations on a Quaternion. No extended knowledge of Quaternions is neccesary for the use of this library. If you like to get familiar with Quaternions, I recommend the relevant Wikipedia article: https://en.wikipedia.org/wiki/Quaternion.
Library Dependencies
Because some vector based math is required to calculate Quaterions, I provide the appropriate Vector library needed to use the Quaternion library here:
https://github.com/MauriceGit/Vector_Library.
Just place both the mtVector.c and mtVector.h in the same directory and compile it with your project.
Interface
The following functions are provided by this library.
Low level Quaternion operations
| Function | Description |
|---|---|
MTQuaternion mtCreateMTQuaternion (MTVec3D axis, double angle) |
Creates a new Quaternion and returns it. |
MTQuaternion mtMultMTQuaternionMTQuaternion (const MTQuaternion* q1, const MTQuaternion* q2) |
Multiplies two Quaternions with each other and returns a new Quaternion. |
MTQuaternion mtMultMTQuaternionScalar (const MTQuaternion* q1, double s) |
Multiplies a Quaternion with a scalar and returnes a new Quaternion. |
MTQuaternion mtAddMTQuaternionMTQuaternion (const MTQuaternion* q1, const MTQuaternion* q2) |
Adds two Quaternions with eath other and returnes a new Quaternion. |
MTQuaternion mtSubtractMTQuaternionMTQuaternion (const MTQuaternion* q1, const MTQuaternion* q2) |
Subtracts a Quaternion q2 from a Quaternion q1. Returnes new Quaternion. |
MTQuaternion mtConjugateMTQuaternion (const MTQuaternion* q1) |
Complex conjugates a Quaternion. Returnes new, conjugated Quaternion. |
MTQuaternion mtInverseMTQuaternion (const MTQuaternion* q1) |
Calculates the inverse of a Quaternion and returnes a a new inverted Quaternion. |
void mtNormMTQuaternion (MTQuaternion* q1) |
Normalises a Quaternion. |
double mtLengthMTQuaternion (const MTQuaternion* q1) |
Calculates the length of a Quaternion. |
int mtIsNormMTQuaternion (const MTQuaternion* q1) |
Checks, if a Quaternion is normalised. |
High level Quaternion operations
| Function | Description |
|---|---|
MTVec3D mtRotatePointWithMTQuaternion (MTQuaternion q, MTVec3D point) |
Rotates a given point with a given Quaternion and returnes a new point. |
MTVec3D mtRotatePointAxis (MTVec3D axis, double angle, MTVec3D point) |
Given an axis, angle and a point, the return value will equal the given point, rotated around the given axis at a given angle (counter-clocwise). |
Usage
An example usage for a Quaternion could be, to rotate a given Point around a given axis, using Quaternions.
Low level approach
// define normalised axis
MTVec3D axis = {0.0, 1.0, 0.0};
// define angle
double angle = 0.1;
// define point to rotate
MTVec3D point = {35.0, -28.3, 5.9};
// create Quaternion from axis and angle
Quaternion q;
q.s = cos (angle/2.0);
q.v = mtMultiplyVectorScalar(axis, sin(angle/2.0))
mtNormMTQuaternion(&q);
// Create MTQuaternion of the point to rotate
MTQuaternion p;
p.s = 0.0;
p.v = point;
// The actual calculations.
// --- q p q* ---
MTQuaternion inverseQ = mtInverseMTQuaternion(&q);
MTQuaternion res = mtMultMTQuaternionMTQuaternion (&q, &p);
res = mtMultMTQuaternionMTQuaternion (&res, &inverseQ);
// Write new rotated coordinates back to the point
point = res.v;
High level approach
MTVec3D axis = {100.9, -35.0, 3.0};
double angle = 0.1;
MTVec3D point = {0.5, 4.9, 1.0};
// The rotated coordinates will be written back to point.
point = mtRotatePointAxis (axis, angle, point);