ShapeMath.h File Reference

Handy math functions for the collision module.

#include <d3d11_2.h>
#include <dxgi1_3.h>
#include <DirectXMath.h>
#include "SimpleMath.h"

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Macros
#define	FailIf(x)

Functions
float	Shapes::NormalizeAngle (float)
	Normalize angle to \([0, 2\pi)\).
Vector2	Shapes::Normalize (Vector2)
	Normalize a vector, ie. make it unit length.
Vector2	Shapes::perp (const Vector2 &)
	Perpendicular vector.
Vector2	Shapes::AngleToVector (const float)
	Normal vector from orientation.
Vector2	Shapes::RotatePt (Vector2, const Vector2 &, const float)
	Rotate point.
Vector2	Shapes::ParallelComponent (const Vector2 &, const Vector2 &)
	Compute parallel component of vector.

Macro Definition Documentation

FailIf

#define FailIf

(

x

)

Value:

if(x)return false;

Fail by returning false if a given condition is true.

Parameters

x	Condition for failure.

Function Documentation

AngleToVector()

Vector2 Shapes::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.

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Normalize()

Vector2 Shapes::Normalize

(

Vector2

v

)

The DirectXTK doesn't have a function that returns a normalized vector, so here it is. We will now be able to use it in constant declarations, for example, const Vector2 u = v.Normalize().

Parameters

v

A vector.

Returns

A unit vector that points in the direction of v.

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NormalizeAngle()

float Shapes::NormalizeAngle

(

float

a

)

Normalize angle to \([0, 2\pi)\).

Parameters

a	Angle in radians.

Returns

Normalized angle, that is, in the range \([0, 2\pi)\).

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ParallelComponent()

Vector2 Shapes::ParallelComponent	(	const Vector2 &	v0,
		const Vector2 &	v1 )

Find the component of one vector parallel to another. The component of \(\vec{v}_0\) parallel to \(\vec{v}_1\) is \((\vec{v}_0 \cdot \hat{v}_1)\hat{v}_1\).

Parameters

v0	Vector whose component we want.
v1	Vector that the component must be parallel to.

Returns

Component of v0 that is parallel to v1.

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perp()

Vector2 Shapes::perp

(

const Vector2 &

v

)

Compute the counterclockwise perpendicular of a vector, preserving length. 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 \(\vec{v}\).

Parameters

v	A vector, not necessarily normalized.

Returns

The counterclockwise perpendicular to v of the same length.

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RotatePt()

Vector2 Shapes::RotatePt	(	Vector2	u,
		const Vector2 &	v,
		const float	a )

Rotate a point about an arbitrary center.

Parameters

u	Point to be rotated.
v	Center of rotation.
a	Angle of rotation in radians counterclockwise.

Returns

Rotated point.

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