Helpers.cpp File Reference

Code for helper functions. More...

#include "Helpers.h"

Functions
const Vector2	AngleToVector (const float theta)
	Convert angle to vector. More...
const Vector2	VectorNormalCC (const Vector2 &v)
	Counterclockwise normal. More...
void	NormalizeAngle (float &theta)
	Normalize angle to \(\pm\pi\). More...

Function Documentation

AngleToVector()

const Vector2 AngleToVector

(

const float

theta

)

Compute a unit vector at an angle measured in radians counterclockwise from the positive X-axis. If \(\vec{v} = [v_x, v_y]\) is a unit vector with tail at the Origin and \(\theta\) is the angle between \(\vec{v}\) and the positive X-axis, then \(\sin \theta = v_y\) and \(\cos \theta = v_x\). Hence, \(\vec{v} = [\cos \theta, \sin \theta]\), as shown below. Therefore, this function returns Vector2(cosf(theta), sinf(theta)).

Parameters

theta

Angle in radians.

Returns

Unit vector at angle theta counterclockwise from positive X.

NormalizeAngle()

void NormalizeAngle

(

float &

theta

)

Normalize an angle in radians to \(\pm\pi\). If the angle is very large or very small, then this function will be very slow. However, it will be very fast if the angle is not too far out of range.

Parameters

theta

[in, out] An angle in radians.

VectorNormalCC()

const Vector2 VectorNormalCC

(

const Vector2 &

v

)

Compute the counterclockwise unit perpendicular to a vector. If \(\vec{v} = [v_x, v_y]\), then both dot products \(\vec{v} \cdot [-v_y, v_x]\) and \(\vec{v} \cdot [v_y, -v_x]\) are equal to zero, and therefore both \([-v_y, v_x]\) and \([v_y, -v_x]\) are perpendicular to \(\vec{v}\). The former (drawn in green below) points counterclockwise from \(\vec{v}\) and the latter (drawn in purple below) points clockwise from \(\vec{v}\). Therefore, this function computes Vector2(-v.y, v.x) and normalizes it before returning it.

Parameters

v	A vector, not necessarily normalized.

Returns

The counterclockwise unit perpendicular to v.