util

func AngleBetweenLines ¶

func AngleBetweenLines(p1, p2, p3, p4 []float64) (float64, 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]. The angle of each line is also returned.

func AngleBisect ¶

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

AngleBisect calcuates the angle of bisection between two lines and returns the absolute and relative angles.

func AngleInRange ¶

func AngleInRange(a, r, b float64) bool

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

func BBCombine ¶

func BBCombine(bb [][]float64, bbs ...[][]float64) [][]float64

BBCombine combines a list of bounding boxes.

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 BBIntersection ¶

func BBIntersection(bb1, bb2 [][]float64) [][]float64

BBIntersection returns the bb formed by the overlap or nil.

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 BBToRect ¶

func BBToRect(bb [][]float64) image.Rectangle

BBToRect converts a bounding box to an image.Rectangle

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 vertex 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 Coincident ¶

func Coincident(lp1, lp2, lp3, lp4 []float64) bool

True if lines are on the same infinite line

func Collinear ¶

func Collinear(lp1, lp2, p []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 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 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 Left ¶

func Left(lp1, lp2, p []float64) bool

Left returns true if p is to the left of the line

func LeftOn ¶

func LeftOn(lp1, lp2, p []float64) bool

Left returns true if p is to the left of or on the line

func Lerp ¶

func Lerp(t, start, end float64) float64

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

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 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 Parallel ¶

func Parallel(lp1, lp2, lp3, lp4 []float64) bool

True if lines are parallel

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 PointInTriangleStrict ¶

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

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

func PointOnLine ¶

func PointOnLine(lp1, lp2, p []float64) (bool, float64)

PointOnLine returns if p is on the line and t for p if it is.

func PointOnTriangle ¶

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

PointOnTriangle returns true if p is on an edge of 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 Right ¶

func Right(lp1, lp2, p []float64) bool

Right returns true if p is to the right of the line

func RightOn ¶

func RightOn(lp1, lp2, p []float64) bool

RightOn returns true if p is to the right of or 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.