Interpolation math. More...

#include <Quat.h>

Inheritance diagram for honey::Interp_< Real >:

Collaboration diagram for honey::Interp_< Real >:

Static Public Member Functions
template<class T >
static T	linear (Real t, const T &a, const T &b)
	Linear interpolation. t range is [0,1]. More...

static Quat	linear (Real t, const Quat &a, const Quat &b)

static Transform	linear (Real t, const Transform &a, const Transform &b)

static Real	linearAngle (Real t, Real angleStart, Real angleEnd, optional< int & > rotSign=optnull)
	Linearly interpolate angles along the shortest path. Angles must be normalized. `t` range is [0,1]. rotSign is the direction rotated: (-ve, +ve, none) = (-1,1,0) More...

static void	alignDir (Vec3 &dir, const Vec3 &targetDir, Real angleAmount, optional< int & > rotSign=optnull)
	Align a normalized direction towards a target direction, rotating around the Y axis, stepping angleAmount. rotSign is the direction rotated: (-ve, +ve, none) = (-1,1,0) More...

template<class T >
static T	baryCentric (Real f, Real g, const T &x0, const T &x1, const T &x2)
	Triangular bary-centric interpolation. More...

static Quat	baryCentric (Real f, Real g, const Quat &q0, const Quat &q1, const Quat &q2)

static Transform	baryCentric (Real f, Real g, const Transform &tm0, const Transform &tm1, const Transform &tm2)

template<class Range , class Seq >
static auto	blend (Range &&vals, Seq &&weights_) -> mt_elemOf(vals)
	Linearly blend a range of values by applying an associated weight to each value. If all weights are 0 then the first value is returned. More...

static Real	sin (Real t, bool smoothIn, bool smoothOut)
	Sin interpolation. More...

static Real	gaussian (Real x, Real offset, Real scale)
	Gaussian / Normal distribution. The standard distribution parameters are (offset, scale) = (0, 1) More...

template<class T >
static MatrixBase< T >::MatrixS	gaussian (const MatrixBase< T > &x, const MatrixBase< T > &offset, const MatrixBase< T > &scale)
	Perform gaussian for each element. More...

template<class T >
static T	bezier (Real t, const T &v0, const T &v1, const T &v2, const T &v3)
	Interpolate along a Bezier curve passing through v0 and v3, using handles (control points) v1 and v2. The handles shape the curve and typically don't lie on it. More...

static tuple< Vec3, int >	bezierRoots (Real y, Real v0, Real v1, Real v2, Real v3)
	Find roots of bezier function at y-intercept `y` More...

static tuple< Vec2, Vec2 >	bezierNormalizeHandles (const Vec2 &v0, const Vec2 &v1, const Vec2 &v2, const Vec2 &v3)
	Given a bezier curve with dim (time, value), normalize the handles (v1,v2) such that there is only 1 root at any point along the time axis. More...

static Real	bezierAtTime (Real time, const Vec2 &v0, const Vec2 &v1, const Vec2 &v2, const Vec2 &v3)
	Given a bezier curve with dim (time, value), get value on curve parameterized by `time` in range [0,1]. More...

static Real	bezierAngleAtTime (Real time, const Vec2 &v0, const Vec2 &v1, const Vec2 &v2, const Vec2 &v3)
	Similar to bezierAtTime() except the value is interpolated by taking the shortest angular path. More...

static void	bezierSubdiv (vector< Vec2 > &cs, int index, Real t)
	Subdivide a bezier curve segment at index (4 control points) by curve param 't' [0,1]. Replaces curve segment with equivalent left/right segments (7 control points) More...

static Real	bezierSubdivAdapt (vector< Vec2 > &cs, int index, Real tol=0.01)
	Adaptively subdivide a bezier curve segment at index (4 control points). Subdivides curve segment until the arc length does not change more than the given tolerance. More...

static Matrix4	bezierPatchCoeff (const Matrix4 &val)
	Bezier 2D patch coefficient matrix generator. More...

static Real	bezierPatch (const Matrix4 &coeff, Real x, Real y)
	Bezier 2D patch interpolation. More...

template<class T >
static T	catmull (Real t, const T &v0, const T &v1, const T &v2, const T &v3)
	Interpolate along a Catmull-Rom curve passing through v1 and v2, using handles (control points) v0 and v3. The spline (piecewise curve) will pass through all control points. More...

static Matrix4	catmullPatchCoeff (const Matrix4 &val)
	Catmull-rom 2D patch coefficient matrix generator. More...

static Real	catmullPatch (const Matrix4 &coeff, Real x, Real y)
	Catmull-rom 2D patch interpolation. More...

Detailed Description

template<class Real>
class honey::Interp_< Real >

Interpolation math.

Member Function Documentation

template<class Real >

void honey::Interp_< Real >::alignDir	(	Vec3 &	dir,
		const Vec3 &	targetDir,
		Real	angleAmount,
		optional< int & >	rotSign = `optnull`
	)

static

Align a normalized direction towards a target direction, rotating around the Y axis, stepping angleAmount. rotSign is the direction rotated: (-ve, +ve, none) = (-1,1,0)

template<class Real >

template<class T >

static T honey::Interp_< Real >::baryCentric	(	Real	f,
		Real	g,
		const T &	x0,
		const T &	x1,
		const T &	x2
	)

inlinestatic

Triangular bary-centric interpolation.

Input -> Output:

(0,0)    -> x0          (1,0) -> x1         (0,1) -> x2
1-f-g==0 -> line x1,x2  (f,0) -> line x0,x1 (0,g) -> line x0,x2

template<class Real >

static Quat honey::Interp_< Real >::baryCentric	(	Real	f,
		Real	g,
		const Quat &	q0,
		const Quat &	q1,
		const Quat &	q2
	)

inlinestatic

template<class Real >

static Transform honey::Interp_< Real >::baryCentric	(	Real	f,
		Real	g,
		const Transform &	tm0,
		const Transform &	tm1,
		const Transform &	tm2
	)

inlinestatic

template<class Real >

template<class T >

static T honey::Interp_< Real >::bezier	(	Real	t,
		const T &	v0,
		const T &	v1,
		const T &	v2,
		const T &	v3
	)

inlinestatic

Interpolate along a Bezier curve passing through v0 and v3, using handles (control points) v1 and v2. The handles shape the curve and typically don't lie on it.

Parameters

t	distance along curve [0-1]
v0	start point
v1	start handle
v2	end handle
v3	end point

Returns: interpolated value

template<class Real >

Real honey::Interp_< Real >::bezierAngleAtTime	(	Real	time,
		const Vec2 &	v0,
		const Vec2 &	v1,
		const Vec2 &	v2,
		const Vec2 &	v3
	)

static

Similar to bezierAtTime() except the value is interpolated by taking the shortest angular path.

template<class Real >

Real honey::Interp_< Real >::bezierAtTime	(	Real	time,
		const Vec2 &	v0,
		const Vec2 &	v1,
		const Vec2 &	v2,
		const Vec2 &	v3
	)

static

Given a bezier curve with dim (time, value), get value on curve parameterized by time in range [0,1].

template<class Real >

auto honey::Interp_< Real >::bezierNormalizeHandles	(	const Vec2 &	v0,
		const Vec2 &	v1,
		const Vec2 &	v2,
		const Vec2 &	v3
	)

static

Given a bezier curve with dim (time, value), normalize the handles (v1,v2) such that there is only 1 root at any point along the time axis.

template<class Real >

static Real honey::Interp_< Real >::bezierPatch	(	const Matrix4 &	coeff,
		Real	x,
		Real	y
	)

inlinestatic

Bezier 2D patch interpolation.

Parameters

coeff	patch coefficient matrix
x	eval point X [0-1]
y	eval point Y [0-1]

Returns: interpolated value

See also: bezierPatchCoeff() to generate coeff

template<class Real >

static Matrix4 honey::Interp_< Real >::bezierPatchCoeff ( const Matrix4 & val )

inlinestatic

Bezier 2D patch coefficient matrix generator.

Parameters

val	a 4x4 grid of control points to interpolate

Return values

patch

See also: bezierPatch() to evaluate patch

template<class Real >

auto honey::Interp_< Real >::bezierRoots	(	Real	y,
		Real	v0,
		Real	v1,
		Real	v2,
		Real	v3
	)

static

Find roots of bezier function at y-intercept y

Return values

roots
rootCount

template<class Real >

void honey::Interp_< Real >::bezierSubdiv	(	vector< Vec2 > &	cs,
		int	index,
		Real	t
	)

static

Subdivide a bezier curve segment at index (4 control points) by curve param 't' [0,1]. Replaces curve segment with equivalent left/right segments (7 control points)

template<class Real >

Real honey::Interp_< Real >::bezierSubdivAdapt	(	vector< Vec2 > &	cs,
		int	index,
		Real	tol = `0.01`
	)

static

Adaptively subdivide a bezier curve segment at index (4 control points). Subdivides curve segment until the arc length does not change more than the given tolerance.

Returns: Bezier curve arc length

template<class Real >

template<class Range , class Seq >

static auto honey::Interp_< Real >::blend	(	Range &&	vals,
		Seq &&	weights_
	)		-> mt_elemOf(vals)

inlinestatic

Linearly blend a range of values by applying an associated weight to each value. If all weights are 0 then the first value is returned.

template<class Real >

template<class T >

static T honey::Interp_< Real >::catmull	(	Real	t,
		const T &	v0,
		const T &	v1,
		const T &	v2,
		const T &	v3
	)

inlinestatic

Interpolate along a Catmull-Rom curve passing through v1 and v2, using handles (control points) v0 and v3. The spline (piecewise curve) will pass through all control points.

Parameters

t	distance along curve [0-1]
v0	start handle
v1	start point
v2	end point
v3	end handle

Returns: interpolated value

template<class Real >

static Real honey::Interp_< Real >::catmullPatch	(	const Matrix4 &	coeff,
		Real	x,
		Real	y
	)

inlinestatic

Catmull-rom 2D patch interpolation.

Parameters

coeff	patch coefficient matrix
x	eval point X [0-1]
y	eval point Y [0-1]

Returns: interpolated value

See also: catmullPatchCoeff() to generate coeff

template<class Real >

static Matrix4 honey::Interp_< Real >::catmullPatchCoeff ( const Matrix4 & val )

inlinestatic

Catmull-rom 2D patch coefficient matrix generator.

Parameters

val	a 4x4 grid of control points to interpolate

Return values

patch

See also: catmullPatch() to evaluate patch

template<class Real >

static Real honey::Interp_< Real >::gaussian	(	Real	x,
		Real	offset,
		Real	scale
	)

inlinestatic

Gaussian / Normal distribution. The standard distribution parameters are (offset, scale) = (0, 1)

template<class Real >

template<class T >

static MatrixBase<T>::MatrixS honey::Interp_< Real >::gaussian	(	const MatrixBase< T > &	x,
		const MatrixBase< T > &	offset,
		const MatrixBase< T > &	scale
	)

inlinestatic

Perform gaussian for each element.

template<class Real >

template<class T >

static T honey::Interp_< Real >::linear	(	Real	t,
		const T &	a,
		const T &	b
	)

inlinestatic

Linear interpolation. t range is [0,1].

template<class Real >

static Quat honey::Interp_< Real >::linear	(	Real	t,
		const Quat &	a,
		const Quat &	b
	)

inlinestatic

template<class Real >

static Transform honey::Interp_< Real >::linear	(	Real	t,
		const Transform &	a,
		const Transform &	b
	)

inlinestatic

template<class Real >

Real honey::Interp_< Real >::linearAngle	(	Real	t,
		Real	angleStart,
		Real	angleEnd,
		optional< int & >	rotSign = `optnull`
	)

static

Linearly interpolate angles along the shortest path. Angles must be normalized. t range is [0,1]. rotSign is the direction rotated: (-ve, +ve, none) = (-1,1,0)

template<class Real >

static Real honey::Interp_< Real >::sin	(	Real	t,
		bool	smoothIn,
		bool	smoothOut
	)

inlinestatic

Sin interpolation.

Parameters

t	distance along curve [0,1]
smoothIn	whether to accelerate into the curve starting at 0
smoothOut	whether to decelerate out of the curve ending at 1

Returns: interpolated value in range [0,1]

The documentation for this class was generated from the following files:

src/common/Honey/Math/Alge/Quat.h
src/common/Honey/Math/NumAnalysis/Interp.h
src/common/Honey/Math/NumAnalysis/Interp.cpp

Static Public Member Functions

Detailed Description

template<class Real> class honey::Interp_< Real >

Member Function Documentation

template<class Real>
class honey::Interp_< Real >