util

package
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 Go to latest Published: Jan 10, 2024 License: Apache-2.0 Imports: 5 Imported by: 2

Documentation

Overview

Package util contains functions for linear and non-linear interpolations and their inversions.

Index

Constants

View Source 
const (
	OddEven wrule = iota
	NonZero
)
View Source 
const (
	Epsilon float64 = 0.000001 // 1:1,000,000
)

%f formats to 6dp by default

View Source 
const (
	TwoPi = math.Pi * 2
)

Variables

View Source 
var WindingRule = OddEven

WindingRule defines how edges in an edge crossing polygon are treated.

Functions

func AngleBetweenLines 

func AngleBetweenLines(p1, p2, p3, p4 []float64) float64

AngleBetweenLines using Atan2 vs calculating the dot product (2xSqrt+Acos). Retains the directionality of the rotation from l1 to l2, unlike dot product. The result is in the range [-Pi,Pi].

func AngleInRange 

func AngleInRange(a, r, b float64) bool

AngleInRange returns true if angle b is within [a,a+r].

func BBContains 

func BBContains(p []float64, bb [][]float64) bool

BBContains returns true if p is in bb at the smallest dimensionality.

func BBFilter 

func BBFilter(pts [][]float64, bb [][]float64) [][]float64

BBFilter returns only points from pts that are in bb at the smallest dimensionality.

func BBOutline 

func BBOutline(bb [][]float64) [][]float64

BBOutline returns a rectangle describing bb.

func BBOverlap 

func BBOverlap(bb1, bb2 [][]float64) bool

BBOverlap returns true if bb1 and bb2 overlap at the smallest dimensionality.

func Barycentric 

func Barycentric(p, tp1, tp2, tp3 []float64) (float64, float64, float64)

Barycentric converts a point on the plane into Barycentric weights given three non-coincident points, tp1, tp2 and tp3.

func Bezier1 

func Bezier1(pts [][]float64, t float64) []float64

Bezier1 (flat curve) {p1, p2}

func Bezier2 

func Bezier2(pts [][]float64, t float64) []float64

Bezier2 (quad curve) {p1, c1, p2}

func Bezier3 

func Bezier3(pts [][]float64, t float64) []float64

Bezier3 (cubic curve) {p1, c1, c2, p2}

func Bezier3ToCatmull 

func Bezier3ToCatmull(p1, p2, p3, p4 []float64) []float64

Bezier3ToCatmull converts a cubic bezier to a catmul curve. p1, c1, c2, p2 => t1, p1, p2, t2

func BoundingBox 

func BoundingBox(pts ...[]float64) [][]float64

BoundingBox returns the minimum and maximum dimensional values in a set of points. Bounds are inclusive. The dimensionality of the smallest dimension point is used for all points.

func CalcDerivativeWeights 

func CalcDerivativeWeights(w [][]float64) [][]float64

CalcDerivativeWeights calculates the derivative of the supplied curve. Bezier gradient (differentiation): Order of curve drops by one and new weights are the difference of the original weights scaled by the original order

func CalcExtremities 

func CalcExtremities(points [][]float64) []float64

CalcExtremities finds the extremes of a curve in terms of t.

func CalcNextOrderWeights 

func CalcNextOrderWeights(w [][]float64) [][]float64

CalcNextOrderWeights calculates the weights necessary to represent the supplied curve at next highest order, i.e. curve promotion b2 to b3. Note, there's no inverse.

func CalcPointsForArc 

func CalcPointsForArc(theta float64) [][]float64

CalcPointsForArc takes an arc angle (less than or equal to Pi), and calculates the points for a Bezier cubic to describe it on a circle centered on (0,0) with radius 1. Mid-point of the curve is (1,0) Error increases for values > Pi/2 Returns nil if the angle is zero Ref: https://www.tinaja.com/glib/bezcirc2.pdf

func CatmullToBezier3 

func CatmullToBezier3(tau float64, p1, p2, p3, p4 []float64) []float64

CatmullToBezier3 converts a catmul curve to a cubic bezier. t1, p1, p2, t2 => p1, c1, c2, p2

func Centroid 

func Centroid(pts ...[]float64) []float64

Centroid returns the centroid of a set of points.

func Circumcircle 

func Circumcircle(p1, p2, p3 []float64) []float64

Circumcircle returns the circle (center and radius) that passes through the three points.

func Collinear 

func Collinear(p1, p2, p3 []float64) bool

Collinear returns true if three points are on a line (i.e. if the area of the resultant triangle is 0)

func CrossProduct 

func CrossProduct(p1, p2, p3 []float64) float64

CrossProduct returns the cross product of the three points. Since the inputs are all in the x-y plane (i.e. z = 0), only the magnitude of the resultant z vector is returned (the x and y vectors are both 0).

func Cubic 

func Cubic(t float64, p []float64) float64

Cubic calculates the value of f(t) for t in range [0,1] given the values of t at -1, 0, 1, 2 in p[] fitted to a cubic polynomial: f(t) = at^3 + bt^2 + ct + d. Clamped because it over/undershoots.

func DeCasteljau 

func DeCasteljau(pts [][]float64, t float64) []float64

DeCasteljau uses de Casteljau's algorithm for degree n curves and returns the point and the tangent of the line it's traversing. {p1, c1, c2, c3, ..., p2}

func Dejitter 

func Dejitter(closed bool, pts ...[]float64) [][]float64

Dejitter takes a list of points, greater than three long, and removes the one that forms the smallest area triangle with its adjacent points. If closed is true then the end points are candidates for elimination too.

func DistanceE 

func DistanceE(p1, p2 []float64) float64

DistanceE returns the Euclidean distance between two points.

func DistanceESquared 

func DistanceESquared(p1, p2 []float64) float64

DistanceESquared returns the squared Euclidean distance between two points.

func DistanceESquaredN 

func DistanceESquaredN(p1, p2 []float64) float64

DistanceESquaredN returns the squared Euclidean distance between two points.

func DistanceToLineSquared 

func DistanceToLineSquared(lp1, lp2, p []float64) (float64, []float64, float64)

DistanceToLineSquared calculates the squared Euclidean length of the normal from a point to the line. Returns the distance squared, the line intercept and the t value.

func DotProduct 

func DotProduct(p1, p2, p3, p4 []float64) float64

DotProduct returns the dot product of the two lines, p1-p2 and p3-p4.

func DotProductAngle 

func DotProductAngle(p1, p2, p3, p4 []float64) float64

DotProductAngle returns the angle between two lines using the dot product method. The result is in the range [0,Pi].

func Equals 

func Equals(d1, d2 float64) bool

Equals returns true if two values are within Epsilon of each other.

func Equals32 

func Equals32(d1, d2 float32) bool

Equals32 is the float32 version of Equals.

func EqualsP 

func EqualsP(v1, v2 []float64) bool

EqualsP returns true if two points are equal (upto the extent of shared dimensions).

func IntersectionTVals 

func IntersectionTVals(x1, y1, x2, y2, x3, y3, x4, y4 float64) ([]float64, error)

IntersectionTVals obtains values of t for each line for where they intersect. Actual intersection => both are in [0,1]

func IntersectionTValsP 

func IntersectionTValsP(p1, p2, p3, p4 []float64) ([]float64, error)

IntersectionTValsP obtains values of t for each line for where they intersect. Actual intersection => both are in [0,1]

func InvLerp 

func InvLerp(v, start, end float64) float64

InvLerp performs the inverse of Lerp and returns the value of t for a value v.

func InvLerp32 

func InvLerp32(v, start, end float32) float32

InvLerp32 is a float32 version of InvLerp.

func InvLerpClamp 

func InvLerpClamp(v, start, end float64) float64

InvLerpClamp is a clamped [start, end] version of InvLerp.

func InvLerpClamp32 

func InvLerpClamp32(v, start, end float32) float32

InvLerpClamp32 is a float32 version of InvLerpClamp.

func InvNLerp 

func InvNLerp(v, start, end float64, f NonLinear) float64

InvNLerp performs the inverse of NLerp and returns the value of t for a value v (clamped to [start, end]).

func InvNLerp32 

func InvNLerp32(v, start, end float32, f NonLinear) float32

InvNLerp32 is a float32 version of InvNLerp for Path and x/image/vector

func InverseBarycentric 

func InverseBarycentric(w1, w2, w3 float64, tp1, tp2, tp3 []float64) []float64

InverseBarycentric converts Barycentric weights plus the three non-coincident points back into a point on the plane.

func Kappa 

func Kappa(dpt, d2pt []float64) float64

Kappa from first and second derivatives at a point.

func Kappa1 

func Kappa1(dw, d2w [][]float64, t float64) float64

Kappa1 calculates curvature - note curve must have 2nd order derivative. Radius of curvature at t is 1/kappa(t)

func KappaC 

func KappaC(p1, p2, p3 []float64) float64

KappaC estimates kappa from three points by calculating the center of the circumcircle.

func KappaM 

func KappaM(p1, p2, p3 []float64) float64

KappaM calculates Menger curvature: 4*area / (d(p1, p2).d(p2s, p3).d(p3, p1)) Same result as KappaC but with more square roots...

func Lerp 

func Lerp(t, start, end float64) float64

Lerp returns the value (1-t)*start + t*end.

func Lerp32 

func Lerp32(t, start, end float32) float32

Lerp32 is a float32 version of Lerp.

func LerpClamp 

func LerpClamp(t, start, end float64) float64

LerpClamp is a clamped [0,1] version of Lerp.

func LerpClamp32 

func LerpClamp32(t, start, end float32) float32

LerpClamp32 is a float32 version of LerpClamp.

func LineAngle 

func LineAngle(p1, p2 []float64) float64

LineAngle returns the angle of a line. Result is in range [-Pi, Pi]

func LineNormalToPoint 

func LineNormalToPoint(lp1, lp2, p []float64) ([]float64, float64, float64)

LineNormalToPoint returns the point on the line that's normal to the specified point, in absolute terms and as a t value. The distance from the point to the line is returned too.

func MinD 

func MinD(pts ...[]float64) int

MinD calculates the minimum dimensionality of point set

func NLerp 

func NLerp(t, start, end float64, f NonLinear) float64

NLerp returns the value of the supplied non-linear function at t. Note t is clamped to [0,1]

func NLerp32 

func NLerp32(t, start, end float32, f NonLinear) float32

NLerp32 is a float32 version of NLerp for Path and x/image/vector

func NRM 

func NRM(start float64, f, df func(float64) float64) (float64, error)

NRM is a modified Newton-Raphson root search that bails if t falls outside of the range [0,1] since the curve isn't defined there.

func PointInPoly 

func PointInPoly(pt []float64, poly ...[]float64) bool

PointInPoly returns true is a point is within the polygon defined by the list of vertices according to the setting of WindingRule (OddEven or NonZero).

func PointInTriangle 

func PointInTriangle(p, tp1, tp2, tp3 []float64) bool

PointInTriangle returns true if p is in the triangle formed by tp1, tp2 and tp3.

func RectToBB 

func RectToBB(rect image.Rectangle) [][]float64

RectToBB converts an image.Rectangle to a bounding box

func Remap 

func Remap(v, istart, iend, ostart, oend float64) float64

Remap converts v from one space to another by applying InvLerp to find t in the initial range, and then using t to find v' in the new range.

func Remap32 

func Remap32(v, istart, iend, ostart, oend float32) float32

Remap32 is a float32 version of Remap.

func RemapClamp 

func RemapClamp(v, istart, iend, ostart, oend float64) float64

RemapClamp is a clamped version of Remap.

func RemapClamp32 

func RemapClamp32(v, istart, iend, ostart, oend float32) float32

RemapClamp32 is a float32 version of RemapClamp.

func RemapNL 

func RemapNL(v, istart, iend, ostart, oend float64, fi, fo NonLinear) float64

RemapNL converts v from one space to another by applying InvNLerp to find t in the initial range, and then using t to find v' in the new range.

func RemapNL32 

func RemapNL32(v, istart, iend, ostart, oend float32, fi, fo NonLinear) float32

RemapNL32 is a float32 version of RemapNL for Path and x/image/vector

func SideOfLine 

func SideOfLine(lp1, lp2, p []float64) float64

SideOfLine calculates which side of a line a point is one by calculating the cross product of the vector from the line start to the point with the line's normal. If +ve then one side, -ve the other, 0 - on the line.

func SplitCurve 

func SplitCurve(pts [][]float64, t float64) [][][]float64

SplitCurve splits curve at t into two new curves such that the end of the lhs is the start of the rhs {p1, c1, c2, c3, ..., p2}

func ToF32 

func ToF32(pts ...float64) []float32

ToF32 casts a slice of float64 to float32. Possible loss of resolution.

func ToF64 

func ToF64(pts ...float32) []float64

ToF64 casts a slice of float32 to float64.

func TriArea 

func TriArea(p1, p2, p3 []float64) float64

TriArea returns the signed area of a triangle by finding the determinant of M = {{p1[0] p1[1] 1} 

{p2[0] p2[1] 1}
{p3[0] p3[1] 1}}

func Vec 

func Vec(p1, p2 []float64) []float64

Vec returns the vector joining two points.

func VecMag 

func VecMag(v []float64) float64

VecMag returns the magnitude of the vector.

func VecNormalize 

func VecNormalize(v []float64) []float64

VecNormalize scales a vector to unit length.

func Within 

func Within(d1, d2, e float64) bool

Within returns true if the two values are within e of each other.

Types

type BezierCurve 

type BezierCurve struct {
	Weights    [][]float64
	WeightsDt  [][]float64
	WeightsDt2 [][]float64
	WeightsDt3 [][]float64
}

BezierCurve stores the derivative curve weights.

func NewBezierCurve 

func NewBezierCurve(weights [][]float64) *BezierCurve

NewBezierCurve creates a new BezierCurve with the weights of the first, second and third order derivatives of the supplied curve.

func (*BezierCurve) CurveDt2X 

func (bc *BezierCurve) CurveDt2X(t float64) float64

CurveDt2X returns the X value for the second order derivative of the curve at t.

func (*BezierCurve) CurveDt2Y 

func (bc *BezierCurve) CurveDt2Y(t float64) float64

CurveDt2Y returns the Y value for the second order derivative of the curve at t.

func (*BezierCurve) CurveDt3X 

func (bc *BezierCurve) CurveDt3X(t float64) float64

CurveDt3X returns the X value for the third order derivative of the curve at t.

func (*BezierCurve) CurveDt3Y 

func (bc *BezierCurve) CurveDt3Y(t float64) float64

CurveDt3Y returns the Y value for the third order derivative of the curve at t.

func (*BezierCurve) CurveDtX 

func (bc *BezierCurve) CurveDtX(t float64) float64

CurveDtX returns the X value for the derivative of the curve at t.

func (*BezierCurve) CurveDtY 

func (bc *BezierCurve) CurveDtY(t float64) float64

CurveDtY returns the Y value for the derivative of the curve at t.

func (*BezierCurve) CurveX 

func (bc *BezierCurve) CurveX(t float64) float64

CurveX returns the X value for the curve at t.

func (*BezierCurve) CurveY 

func (bc *BezierCurve) CurveY(t float64) float64

CurveY returns the Y value for the curve at t.

func (*BezierCurve) Kappa 

func (bc *BezierCurve) Kappa(t float64) float64

Kappa calculates the curvature at t. Radius of curvature at t is 1/kappa(t)

type NLCatenary 

type NLCatenary struct{}

NLCatenary v = cosh(t)

func (*NLCatenary) InvTransform 

func (nl *NLCatenary) InvTransform(v float64) float64

func (*NLCatenary) Transform 

func (nl *NLCatenary) Transform(t float64) float64

type NLCircle1 

type NLCircle1 struct{}

NLCircle1 v = 1 - sqrt(1-t^2)

func (*NLCircle1) InvTransform 

func (nl *NLCircle1) InvTransform(v float64) float64

func (*NLCircle1) Transform 

func (nl *NLCircle1) Transform(t float64) float64

type NLCircle2 

type NLCircle2 struct{}

NLCircle2 v = sqrt(2t-t^2)

func (*NLCircle2) InvTransform 

func (nl *NLCircle2) InvTransform(v float64) float64

func (*NLCircle2) Transform 

func (nl *NLCircle2) Transform(t float64) float64

type NLCompound 

type NLCompound struct {
	Fs []NonLinear
}

NLCompound v = nl[0](nl[1](nl[2](...nl[n-1](t))))

func NewNLCompound 

func NewNLCompound(fs []NonLinear) *NLCompound

func (*NLCompound) InvTransform 

func (nl *NLCompound) InvTransform(v float64) float64

func (*NLCompound) Transform 

func (nl *NLCompound) Transform(t float64) float64

type NLCube 

type NLCube struct{}

NLCube v = t^3

func (*NLCube) InvTransform 

func (nl *NLCube) InvTransform(v float64) float64

func (*NLCube) Transform 

func (nl *NLCube) Transform(t float64) float64

type NLExponential 

type NLExponential struct {
	K     float64
	Scale float64
}

NLExponential v = (exp(t*k) - 1) * scale

func NewNLExponential 

func NewNLExponential(k float64) *NLExponential

func (*NLExponential) InvTransform 

func (nl *NLExponential) InvTransform(v float64) float64

func (*NLExponential) Transform 

func (nl *NLExponential) Transform(t float64) float64

type NLGauss 

type NLGauss struct {
	K, Offs, Scale float64
}

NLGauss v = gauss(t, k)

func NewNLGauss 

func NewNLGauss(k float64) *NLGauss

func (*NLGauss) InvTransform 

func (nl *NLGauss) InvTransform(v float64) float64

func (*NLGauss) Transform 

func (nl *NLGauss) Transform(t float64) float64

type NLLinear 

type NLLinear struct{}

NLLinear v = t

func (*NLLinear) InvTransform 

func (nl *NLLinear) InvTransform(v float64) float64

func (*NLLinear) Transform 

func (nl *NLLinear) Transform(t float64) float64

type NLLogarithmic 

type NLLogarithmic struct {
	K     float64
	Scale float64
}

NLLogarithmic v = log(1+t*k) * scale

func NewNLLogarithmic 

func NewNLLogarithmic(k float64) *NLLogarithmic

func (*NLLogarithmic) InvTransform 

func (nl *NLLogarithmic) InvTransform(v float64) float64

func (*NLLogarithmic) Transform 

func (nl *NLLogarithmic) Transform(t float64) float64

type NLLogistic 

type NLLogistic struct {
	K, Mp, Offs, Scale float64
}

NLLogistic v = logistic(t, k, mp)

func NewNLLogistic 

func NewNLLogistic(k, mp float64) *NLLogistic

k > 0 and mp (0,1) - not checked

func (*NLLogistic) InvTransform 

func (nl *NLLogistic) InvTransform(v float64) float64

func (*NLLogistic) Transform 

func (nl *NLLogistic) Transform(t float64) float64

type NLOmt 

type NLOmt struct {
	F NonLinear
}

NLOmt v = 1-f(1-t)

func NewNLOmt 

func NewNLOmt(f NonLinear) *NLOmt

func (*NLOmt) InvTransform 

func (nl *NLOmt) InvTransform(v float64) float64

func (*NLOmt) Transform 

func (nl *NLOmt) Transform(t float64) float64

type NLP3 

type NLP3 struct{} // first derivative 0 at t=0,1

NLP3 v = t^2 * (3-2t)

func (*NLP3) InvTransform 

func (nl *NLP3) InvTransform(v float64) float64

func (*NLP3) Transform 

func (nl *NLP3) Transform(t float64) float64

type NLP5 

type NLP5 struct{} // first and second derivatives 0 at t=0,1

NLP5 v = t^3 * (t*(6t-15) + 10)

func (*NLP5) InvTransform 

func (nl *NLP5) InvTransform(v float64) float64

func (*NLP5) Transform 

func (nl *NLP5) Transform(t float64) float64

type NLRand 

type NLRand struct {
	Steps []float64
	Dt    float64
}

NLRand uses random incremental steps from a normal distribution, smoothed with a cubic.

func NewNLRand 

func NewNLRand(mean, std float64, sharp bool) *NLRand

NewRandNL calculates a collection of ascending values [0,1] with an average increment of mean and standard deviation of std.

func (*NLRand) InvTransform 

func (nl *NLRand) InvTransform(v float64) float64

func (*NLRand) Transform 

func (nl *NLRand) Transform(t float64) float64

type NLSin 

type NLSin struct{} // first derivative 0 at t=0,1

NLSin v = sin(t) with t mapped to [-Pi/2,Pi/2]

func (*NLSin) InvTransform 

func (nl *NLSin) InvTransform(v float64) float64

func (*NLSin) Transform 

func (nl *NLSin) Transform(t float64) float64

type NLSin1 

type NLSin1 struct{} // first derivative 0 at t=1

NLSin1 v = sin(t) with t mapped to [0,Pi/2]

func (*NLSin1) InvTransform 

func (nl *NLSin1) InvTransform(v float64) float64

func (*NLSin1) Transform 

func (nl *NLSin1) Transform(t float64) float64

type NLSin2 

type NLSin2 struct{} // first derivative 0 at t=0,1

NLSin2 v = sin(t) with t mapped to [-Pi/2,0]

func (*NLSin2) InvTransform 

func (nl *NLSin2) InvTransform(v float64) float64

func (*NLSin2) Transform 

func (nl *NLSin2) Transform(t float64) float64

type NLSquare 

type NLSquare struct{}

NLSquare v = t^2

func (*NLSquare) InvTransform 

func (nl *NLSquare) InvTransform(v float64) float64

func (*NLSquare) Transform 

func (nl *NLSquare) Transform(t float64) float64

type NLStopped 

type NLStopped struct {
	Stops [][]float64 // Pairs of t, v - both strictly ascending in [0,1]
}

NewStoppedNL uses linear interpolation between the supplied stops

func NewNLStopped 

func NewNLStopped(stops [][]float64) *NLStopped

func (*NLStopped) InvTransform 

func (nl *NLStopped) InvTransform(v float64) float64

func (*NLStopped) Transform 

func (nl *NLStopped) Transform(t float64) float64

type NonLinear 

type NonLinear interface {
	Transform(t float64) float64
	InvTransform(v float64) float64
}

NonLinear interface defines the transform and its inverse as used by NLerp etc. For mapping 0 -> 1 non-linearly. No checks! Only valid in range [0,1]

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