/
shape.go
362 lines (296 loc) · 8.75 KB
/
shape.go
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package geometry
import (
"math"
"math/rand"
"github.com/EliCDavis/vector/vector2"
)
// Shape is a flat (2D) arrangement of points.
type Shape []vector2.Float64
func (s Shape) GetBounds() (vector2.Float64, vector2.Float64) {
bottomLeftX := math.Inf(1)
bottomLeftY := math.Inf(1)
topRightX := math.Inf(-1)
topRightY := math.Inf(-1)
for _, p := range s {
if p.X() < bottomLeftX {
bottomLeftX = p.X()
}
if p.Y() < bottomLeftY {
bottomLeftY = p.Y()
}
if p.X() > topRightX {
topRightX = p.X()
}
if p.Y() > topRightY {
topRightY = p.Y()
}
}
return vector2.New(bottomLeftX, bottomLeftY), vector2.New(topRightX, topRightY)
}
func (s Shape) GetBoundingBoxDimensions() (width, height float64) {
bottomLeft, topRight := s.GetBounds()
return topRight.X() - bottomLeft.X(), topRight.Y() - bottomLeft.Y()
}
// RandomPointInShape returns a random point inside of the shape
func (s Shape) RandomPointInShape() vector2.Float64 {
bottomLeftBounds, topRightBounds := s.GetBounds()
for {
point := vector2.New(
bottomLeftBounds.X()+(rand.Float64()*(topRightBounds.X()-bottomLeftBounds.X())),
bottomLeftBounds.Y()+(rand.Float64()*(topRightBounds.Y()-bottomLeftBounds.Y())),
)
if s.IsInside(point) {
return point
}
}
}
// Split figures out which points land on which side of the vertical line and
// builds new shapes from that
func (s Shape) Split(vericalLine float64) ([]Shape, []Shape) {
return s.shapesOnSide(vericalLine, -1), s.shapesOnSide(vericalLine, 1)
}
func (s Shape) startinPointForSideShape(vericalLine float64, side int) (bool, int) {
startingPointIndex := 0
lowestPointHeight := 1000000.0
lastSide := 0
crossed := false
if s[len(s)-1].X() < vericalLine {
lastSide = -1
} else {
lastSide = 1
}
for i := 0; i < len(s); i++ {
n := i * -1 * side
if n < 0 {
n += len(s)
}
if lastSide == side*-1 && s[n].Y() < lowestPointHeight {
if (side == -1 && s[n].X() < vericalLine) || (side == 1 && s[n].X() > vericalLine) {
lowestPointHeight = s[n].Y()
startingPointIndex = n
}
}
newSide := 0
if s[n].X() <= vericalLine {
newSide = -1
} else {
newSide = 1
}
if lastSide != newSide {
crossed = true
}
lastSide = newSide
}
if crossed == false {
if side == lastSide {
return true, -1
}
return false, -1
}
return false, startingPointIndex
}
func (s Shape) shapesOnSide(vericalLineX float64, side int) []Shape {
onOurSide, startingPointIndex := s.startinPointForSideShape(vericalLineX, side)
if startingPointIndex == -1 {
if onOurSide {
return []Shape{s}
}
return []Shape{}
}
type region struct {
highestPoint float64
lowestPoint float64
points []vector2.Float64
started bool
}
pointBefore := startingPointIndex + side
if pointBefore >= len(s) {
pointBefore -= len(s)
} else if pointBefore < 0 {
pointBefore += len(s)
}
verticalLine := NewLine2D(vector2.New(vericalLineX, -1000000), vector2.New(vericalLineX, 1000000))
curLine := NewLine2D(s[startingPointIndex], s[pointBefore])
intersection, err := verticalLine.Intersection(curLine)
if err == ErrNoIntersection {
panic("Intersection is nil!")
}
regions := []region{{-100000, 100000, make([]vector2.Float64, 1), false}}
regions[0].points[0] = intersection
regions[0].lowestPoint = intersection.Y()
currentRegion := 0
// -1 for left, +1 for right, 0 for unset
lastPointsSide := side
for i := 0; i < len(s); i++ {
n := (i * -1 * side) + startingPointIndex
if n >= len(s) {
n -= len(s)
} else if n < 0 {
n += len(s)
}
var currentSide int
if s[n].X() <= vericalLineX {
currentSide = -1
} else {
currentSide = 1
}
// Change the region we're working with.
if currentSide != lastPointsSide {
pointBefore = n + side
if pointBefore >= len(s) {
pointBefore -= len(s)
} else if pointBefore < 0 {
pointBefore += len(s)
}
intersection, err := NewLine2D(s[n], s[pointBefore]).Intersection(verticalLine)
if err == ErrNoIntersection {
panic("Intersection is nil!")
}
if currentRegion != -1 {
if regions[currentRegion].started == false {
regions[currentRegion].highestPoint = intersection.Y()
}
regions[currentRegion].started = true
}
if currentSide == side {
foundRegion := false
// Find region we're in.
for regionIndex := range regions {
if regions[regionIndex].lowestPoint <= s[n].Y() &&
regions[regionIndex].highestPoint >= s[n].Y() {
currentRegion = regionIndex
foundRegion = true
break
}
}
// If can't find one, create one.
if foundRegion == false {
regions = append(regions, region{-100000, 100000, make([]vector2.Float64, 0), false})
currentRegion = len(regions) - 1
regions[currentRegion].lowestPoint = intersection.Y()
}
regions[currentRegion].points = append(regions[currentRegion].points, intersection)
} else {
regions[currentRegion].points = append(regions[currentRegion].points, intersection)
currentRegion = -1
}
}
if currentRegion != -1 {
if regions[currentRegion].started == false {
regions[currentRegion].highestPoint = s[n].Y()
}
regions[currentRegion].points = append(regions[currentRegion].points, s[n])
}
lastPointsSide = currentSide
}
resultingShapes := make([]Shape, 0)
for r := range regions {
if len(regions[r].points) > 2 {
resultingShapes = append(resultingShapes, Shape(regions[r].points))
}
}
return resultingShapes
}
// IsInside returns true if the point p lies inside the polygon[] with n vertices
func (s Shape) IsInside(p vector2.Float64) bool {
// There must be at least 3 vertices in polygon[]
if len(s) < 3 {
return false
}
// Create a point for line segment from p to infinite
extreme := vector2.New(math.MaxFloat64, p.Y())
// Count intersections of the above line with sides of polygon
count := 0
i := 0
for {
next := (i + 1) % len(s)
// Check if the line segment from 'p' to 'extreme' intersects
// with the line segment from 'polygon[i]' to 'polygon[next]'
if NewLine2D(s[i], s[next]).Intersects(NewLine2D(p, extreme)) {
// If the point 'p' is colinear with line segment 'i-next',
// then check if it lies on segment. If it lies, return true,
// otherwise false
if calculateOrientation(s[i], p, s[next]) == Colinear {
return onSegment(s[i], p, s[next])
}
count++
}
i = next
if i == 0 {
break
}
}
// log.Print(count)
// Return true if count is odd, false otherwise
return count%2 == 1
}
// Translate Moves all points over by the specified amount
func (s Shape) Translate(amount vector2.Float64) Shape {
newShapePonts := make([]vector2.Float64, len(s))
for i, point := range s {
newShapePonts[i] = point.Add(amount)
}
return Shape(newShapePonts)
}
// Rotate will rotate all points in the shape around the pivot by the passed in amount
func (s Shape) Rotate(amount float64, pivot vector2.Float64) Shape {
newPoints := make([]vector2.Float64, s.Len())
for p, point := range s {
// https://play.golang.org/p/qWUotd3Lb56
directionWithMag := point.Sub(pivot)
magnitude := directionWithMag.Length()
newRot := math.Atan2(directionWithMag.Y(), directionWithMag.X()) + amount
newPoints[p] = vector2.New(
math.Cos(newRot)*magnitude,
math.Sin(newRot)*magnitude,
).Add(pivot)
}
return Shape(newPoints)
}
// Scale shifts all points towards or away from the origin
func (s Shape) Scale(amount float64, origin vector2.Float64) Shape {
newShapePonts := make([]vector2.Float64, len(s))
for i, point := range s {
newShapePonts[i] = origin.Add(point.Sub(origin).Normalized().Scale(amount * origin.Distance(point)))
}
return newShapePonts
}
// Len returns the number of points in the polygon
func (s Shape) Len() int {
return len(s)
}
// Swap switches two points indeces so the polygon is ordered a different way
func (s Shape) Swap(i, j int) {
s[i], s[j] = s[j], s[i]
}
// Less determines which point is more oriented more clockwise from the center than the other
func (s Shape) Less(i, j int) bool {
center := vector2.Zero[float64]()
a := s[i]
b := s[j]
if a.X()-center.X() >= 0 && b.X()-center.X() < 0 {
return true
}
if a.X()-center.X() < 0 && b.X()-center.X() >= 0 {
return false
}
if a.X()-center.X() == 0 && b.X()-center.X() == 0 {
if a.Y()-center.Y() >= 0 || b.Y()-center.Y() >= 0 {
return a.Y() > b.Y()
}
return b.Y() > a.Y()
}
// compute the cross product of vectors (center -> a) x (center -> b)
det := (a.X()-center.X())*(b.Y()-center.Y()) - (b.X()-center.X())*(a.Y()-center.Y())
if det < 0 {
return true
}
if det > 0 {
return false
}
// points a and b are on the same line from the center
// check which point is closer to the center
d1 := (a.X()-center.X())*(a.X()-center.X()) + (a.Y()-center.Y())*(a.Y()-center.Y())
d2 := (b.X()-center.X())*(b.X()-center.X()) + (b.Y()-center.Y())*(b.Y()-center.Y())
return d1 > d2
}