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geometry.go
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geometry.go
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package geometry
import (
"fmt"
"math"
)
func Degree2Radian(degree float64) float64 { return math.Pi * degree / 180 }
func Radian2Degree(radian float64) float64 { return radian * 180 / math.Pi }
type Point complex128
func P(x, y float64) Point { return Point(complex(x, y)) }
func Float(f float64) Point { return Point(complex(f, 0)) }
func (p Point) String() string { return fmt.Sprintf("(%g,%g)", p.X(), p.Y()) }
func (p Point) X() float64 { return real(p) }
func (p Point) Y() float64 { return imag(p) }
func (p Point) Square() float64 { return p.X()*p.X() + p.Y()*p.Y() }
func (p Point) SquareTo(p2 Point) float64 { return (p - p2).Square() }
func (p Point) Len() float64 { return math.Sqrt(p.Square()) }
func (p Point) Dist(p2 Point) float64 { return (p - p2).Len() }
func (p Point) Radian() float64 {
x, y := p.X(), p.Y()
if x == 0 || y == 0 {
return 0
}
if x == 0 {
if y > 0 {
return math.Pi / 2
} else {
return math.Pi + math.Pi/2
}
}
r := math.Atan(y / x)
if x > 0 {
if y >= 0 {
return r
} else {
return 2*math.Pi + r
}
} else {
return math.Pi + r
}
}
type Matrix [2][2]float64
func NewMatrix(v00, v01, v10, v11 float64) Matrix {
var m Matrix
m[0][0] = v00
m[0][1] = v01
m[1][0] = v10
m[1][1] = v11
return m
}
func Rotate(radian float64) Matrix {
cosv := math.Cos(radian)
sinv := math.Sin(radian)
return NewMatrix(cosv, -sinv, sinv, cosv)
}
func (m Matrix) Mul(m2 Matrix) Matrix {
v00 := m[0][0]*m2[0][0] + m[0][1]*m2[1][0]
v01 := m[0][0]*m2[0][1] + m[0][1]*m2[1][1]
v10 := m[1][0]*m2[0][0] + m[1][1]*m2[1][0]
v11 := m[1][0]*m2[0][1] + m[1][1]*m2[1][1]
return NewMatrix(v00, v01, v10, v11)
}
func (m Matrix) String() string {
const format = `+---------+---------+
| %7.1f | %7.1f |
+---------+---------+
| %7.1f | %7.1f |
+---------+---------+`
return fmt.Sprintf(format, m[0][0], m[0][1], m[1][0], m[1][1])
}
type Bezier struct {
points []Point
radians []float64
}
func (b Bezier) Points() []Point { return b.points }
func (b Bezier) Radians() []float64 { return b.radians }
func NewBezier(points []Point, length float64) *Bezier {
if len(points) < 2 {
return nil
}
if len(points) == 3 {
return newBezier3(points, length)
}
if len(points) == 4 {
return newBezier4(points, length)
}
bezier := new(Bezier)
bezier.points = append(bezier.points, points[0])
var (
count = len(points) - 1
p1 Point
length2 = length * length
)
for i := 0; i < 1000; i++ {
index := 0
t := float64(i) / 1000
for index < count {
k := math.Pow(t, float64(index))
k *= math.Pow(1-t, float64(count-index))
k *= float64(combination(int64(count), int64(index)))
p1 = p1 + (points[index] * Float(k))
index++
}
last := bezier.points[len(bezier.points)-1]
dist2 := last.SquareTo(p1)
if dist2 > length2 {
bezier.points = append(bezier.points, p1)
bezier.radians = append(bezier.radians, (p1 - last).Radian())
}
}
return bezier
}
func newBezier3(points []Point, length float64) *Bezier {
bezier := new(Bezier)
bezier.points = append(bezier.points, points[0])
var (
p1 Point
length2 = length * length
)
for i := 0; i < 1000; i++ {
t := float64(i) / 1000
t2 := t * t
k0 := t2 - 2*t + 1
k1 := 2*t - 2*t2
k2 := t2
p1 = points[0]*Float(k0) + points[1]*Float(k1) + points[2]*Float(k2)
last := bezier.points[len(bezier.points)-1]
dist2 := last.SquareTo(p1)
if dist2 > length2 {
bezier.points = append(bezier.points, p1)
bezier.radians = append(bezier.radians, (p1 - last).Radian())
}
}
return bezier
}
func newBezier4(points []Point, length float64) *Bezier {
bezier := new(Bezier)
bezier.points = append(bezier.points, points[0])
var (
p1 Point
length2 = length * length
)
for i := 0; i < 1000; i++ {
t := float64(i) / 1000
t2 := t * t
t3 := t2 * t
nt := 1 - t
nt2 := nt * nt
nt3 := nt2 * nt
k0 := nt3
k1 := 3 * t * nt2
k2 := 3 * t2 * nt
k3 := t3
p1 = points[0]*Float(k0) + points[1]*Float(k1) + points[2]*Float(k2) + points[3]*Float(k3)
last := bezier.points[len(bezier.points)-1]
dist2 := last.SquareTo(p1)
if dist2 > length2 {
bezier.points = append(bezier.points, p1)
bezier.radians = append(bezier.radians, (p1 - last).Radian())
}
}
return bezier
}
func combination(c, r int64) int64 {
if (r << 1) > c {
r = c - r
}
x := int64(1)
y := int64(1)
for i := int64(0); i < r; i++ {
x *= c - i
}
for i := int64(0); i < r; i++ {
y *= r - i
}
return x / y
}