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Copy pathline.go
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168 lines (141 loc) · 3.49 KB
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package curve
import (
"iter"
"math"
)
// Line represents a line segment. It is both a [Shape] and a [ParametricCurve].
type Line struct {
/// The line's start point.
P0 Point
/// The line's end point.
P1 Point
}
var _ Shape = Line{}
var _ ParametricCurve = Line{}
var _ ArclenSolver = Line{}
// Length returns the length of the line.
func (l Line) Length() float64 {
return l.P1.Sub(l.P0).Hypot()
}
// Arclen returns the length of the line
func (l Line) Arclen(accuracy float64) float64 {
return l.Length()
}
func (l Line) SolveForArclen(arclen float64, accuracy float64) float64 {
return arclen / l.P1.Sub(l.P0).Hypot()
}
// / Computes the point where two lines, if extended to infinity, would cross.
func (l Line) CrossingPoint(o Line) (Point, bool) {
ab := l.P1.Sub(l.P0)
cd := o.P1.Sub(o.P0)
pcd := ab.Cross(cd)
if pcd == 0 {
return Point{}, false
}
h := ab.Cross(l.P0.Sub(o.P0)) / pcd
return o.P0.Translate(cd.Mul(h)), true
}
func (l Line) IsInf() bool {
return l.P0.IsInf() || l.P1.IsInf()
}
func (l Line) IsNaN() bool {
return l.P0.IsNaN() || l.P1.IsNaN()
}
func (l Line) Translate(v Vec2) Line {
return Line{
P0: l.P0.Translate(v),
P1: l.P1.Translate(v),
}
}
func (l Line) BoundingBox() Rect {
return Rect{
X0: l.P0.X,
Y0: l.P0.Y,
X1: l.P1.X,
Y1: l.P1.Y,
}
}
func (l Line) Perimeter(accuracy float64) float64 {
return l.Length()
}
func (l Line) PathElements(tolerance float64) iter.Seq[PathElement] {
return func(yield func(PathElement) bool) {
_ = yield(MoveTo(l.P0)) &&
yield(LineTo(l.P1))
}
}
func (l Line) Eval(t float64) Point {
return l.P0.Lerp(l.P1, t)
}
func (l Line) Nearest(pt Point, accuracy float64) (distSq, t float64) {
d := l.P1.Sub(l.P0)
dotp := d.Dot(pt.Sub(l.P0))
dSquared := d.Dot(d)
if dotp <= 0.0 {
return pt.Sub(l.P0).Hypot2(), 0.0
} else if dotp >= dSquared {
return pt.Sub(l.P1).Hypot2(), 1.0
} else {
t := dotp / dSquared
dist := pt.Sub(l.Eval(t)).Hypot2()
return dist, t
}
}
func (l Line) Transform(aff Affine) Line {
return Line{
P0: l.P0.Transform(aff),
P1: l.P1.Transform(aff),
}
}
func (l Line) Start() Point { return l.P0 }
func (l Line) End() Point { return l.P1 }
func (l Line) Subsegment(start, end float64) Line {
return Line{l.Eval(start), l.Eval(end)}
}
func (l Line) SubsegmentCurve(start, end float64) ParametricCurve {
return l.Subsegment(start, end)
}
func (l Line) Subdivide() (Line, Line) {
return l.Subsegment(0.0, 0.5), l.Subsegment(0.5, 1.0)
}
func (l Line) SubdivideCurve() (ParametricCurve, ParametricCurve) {
return l.Subdivide()
}
func (l Line) Extrema() ([MaxExtrema]float64, int) {
return [MaxExtrema]float64{}, 0
}
func (l Line) SignedArea() float64 {
return Vec2(l.P0).Cross(Vec2(l.P1)) * 0.5
}
func (l Line) Tangents() (Vec2, Vec2) {
d := l.P1.Sub(l.P0)
return d, d
}
func (l Line) Seg() PathSegment {
return PathSegment{Kind: LineKind, P0: l.P0, P1: l.P1}
}
func (l Line) IntersectLine(o Line) ([3]LineIntersection, int) {
const epsilon = 1e-9
p0 := o.P0
p1 := o.P1
dx := p1.X - p0.X
dy := p1.Y - p0.Y
det := dx*(l.P1.Y-l.P0.Y) - dy*(l.P1.X-l.P0.X)
if math.Abs(det) < epsilon {
// Lines are coincident (or nearly so).
return [3]LineIntersection{}, 0
}
t := dx*(p0.Y-l.P0.Y) - dy*(p0.X-l.P0.X)
// t = position on self
t /= det
if t >= -epsilon && t <= 1+epsilon {
// u = position on probe line
u :=
(l.P0.X-p0.X)*(l.P1.Y-l.P0.Y) - (l.P0.Y-p0.Y)*(l.P1.X-l.P0.X)
u /= det
if u >= 0.0 && u <= 1.0 {
return [3]LineIntersection{{u, t}}, 1
}
}
return [3]LineIntersection{}, 0
}