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geom.go
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// Copyright (c) 2011 Mateusz Czapliński (Go port)
// Copyright (c) 2011 Mahir Iqbal (as3 version)
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
// based on http://code.google.com/p/as3polyclip/ (MIT licensed)
// and code by Martínez et al: http://wwwdi.ujaen.es/~fmartin/bool_op.html (public domain)
// Package polyclip provides implementation of algorithm for Boolean operations on 2D polygons.
// For further details, consult the description of Polygon.Construct method.
package polyclip
import (
"math"
"github.com/gonum/floats"
)
type Point struct {
X, Y float64
}
// Equals returns true if both p1 and p2 describe exactly the same point.
func (p1 Point) Equals(p2 Point) bool {
return p1.X == p2.X && p1.Y == p2.Y
}
// EqualWithin returns true if p1 is within tol tolerance of p2
func (p1 Point) EqualWithin(p2 Point, tol float64) bool {
return floats.EqualWithinAbsOrRel(p1.X, p2.X, tol, tol) &&
floats.EqualWithinAbsOrRel(p1.Y, p2.Y, tol, tol)
}
// Length returns distance from p to point (0, 0).
func (p Point) Length() float64 {
return math.Sqrt(p.X*p.X + p.Y*p.Y)
}
type Rectangle struct {
Min, Max Point
}
func (r1 Rectangle) union(r2 Rectangle) Rectangle {
return Rectangle{
Min: Point{
X: math.Min(r1.Min.X, r2.Min.X),
Y: math.Min(r1.Min.Y, r2.Min.Y),
},
Max: Point{
X: math.Max(r1.Max.X, r2.Max.X),
Y: math.Max(r1.Max.Y, r2.Max.Y),
}}
}
// Overlaps returns whether r1 and r2 have a non-empty intersection.
func (r1 Rectangle) Overlaps(r2 Rectangle) bool {
return r1.Min.X <= r2.Max.X && r1.Max.X >= r2.Min.X &&
r1.Min.Y <= r2.Max.Y && r1.Max.Y >= r2.Min.Y
}
// Used to represent an edge of a polygon.
type segment struct {
start, end Point
}
// Contour represents a sequence of vertices connected by line segments, forming a closed shape.
type Contour []Point
// Add is a convenience method for appending a point to a contour.
func (c *Contour) Add(p Point) {
*c = append(*c, p)
}
// BoundingBox finds minimum and maximum coordinates of points in a contour.
func (c Contour) BoundingBox() Rectangle {
bb := Rectangle{}
bb.Min.X = math.Inf(1)
bb.Min.Y = math.Inf(1)
bb.Max.X = math.Inf(-1)
bb.Max.Y = math.Inf(-1)
for _, p := range c {
if p.X > bb.Max.X {
bb.Max.X = p.X
}
if p.X < bb.Min.X {
bb.Min.X = p.X
}
if p.Y > bb.Max.Y {
bb.Max.Y = p.Y
}
if p.Y < bb.Min.Y {
bb.Min.Y = p.Y
}
}
return bb
}
func (c Contour) segment(index int) segment {
if index == len(c)-1 {
return segment{c[len(c)-1], c[0]}
}
return segment{c[index], c[index+1]}
// if out-of-bounds, we expect panic detected by runtime
}
// Checks if a point is inside a contour using the "point in polygon" raycast method.
// This works for all polygons, whether they are clockwise or counter clockwise,
// convex or concave.
// See: http://en.wikipedia.org/wiki/Point_in_polygon#Ray_casting_algorithm
// Returns true if p is inside the polygon defined by contour.
func (c Contour) Contains(p Point) bool {
// Cast ray from p.x towards the right
intersections := 0
for i := range c {
curr := c[i]
ii := i + 1
if ii == len(c) {
ii = 0
}
next := c[ii]
// Is the point out of the edge's bounding box?
// bottom vertex is inclusive (belongs to edge), top vertex is
// exclusive (not part of edge) -- i.e. p lies "slightly above
// the ray"
bottom, top := curr, next
if bottom.Y > top.Y {
bottom, top = top, bottom
}
if p.Y < bottom.Y || p.Y >= top.Y {
continue
}
// Edge is from curr to next.
if p.X >= math.Max(curr.X, next.X) ||
next.Y == curr.Y {
continue
}
// Find where the line intersects...
xint := (p.Y-curr.Y)*(next.X-curr.X)/(next.Y-curr.Y) + curr.X
if curr.X != next.X && p.X > xint {
continue
}
intersections++
}
return intersections%2 != 0
}
// Clone returns a copy of a contour.
func (c Contour) Clone() Contour {
return append([]Point{}, c...)
}
// Polygon is carved out of a 2D plane by a set of (possibly disjoint) contours.
// It can thus contain holes, and can be self-intersecting.
type Polygon []Contour
// NumVertices returns total number of all vertices of all contours of a polygon.
func (p Polygon) NumVertices() int {
num := 0
for _, c := range p {
num += len(c)
}
return num
}
// BoundingBox finds minimum and maximum coordinates of points in a polygon.
func (p Polygon) BoundingBox() Rectangle {
bb := p[0].BoundingBox()
for _, c := range p[1:] {
bb = bb.union(c.BoundingBox())
}
return bb
}
// Add is a convenience method for appending a contour to a polygon.
func (p *Polygon) Add(c Contour) {
*p = append(*p, c)
}
// Clone returns a duplicate of a polygon.
func (p Polygon) Clone() Polygon {
r := Polygon(make([]Contour, len(p)))
for i := range p {
r[i] = p[i].Clone()
}
return r
}
// Op describes an operation which can be performed on two polygons.
type Op int
const (
UNION Op = iota
INTERSECTION
DIFFERENCE
XOR
CLIPLINE // CLIPLINE assumes that the subject polygon is actually a polygon and clips it
)
// Construct computes a 2D polygon, which is a result of performing
// specified Boolean operation on the provided pair of polygons (p <Op> clipping).
// It uses algorithm described by F. Martínez, A. J. Rueda, F. R. Feito
// in "A new algorithm for computing Boolean operations on polygons"
// - see: http://wwwdi.ujaen.es/~fmartin/bool_op.html
// The paper describes the algorithm as performing in time O((n+k) log n),
// where n is number of all edges of all polygons in operation, and
// k is number of intersections of all polygon edges.
func (p Polygon) Construct(operation Op, clipping Polygon) Polygon {
c := clipper{
subject: p,
clipping: clipping,
}
return c.compute(operation)
}