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peel.go
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peel.go
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package main
import (
"math"
"github.com/unixpickle/model3d/model2d"
"github.com/unixpickle/model3d/model3d"
)
const (
PeelLongSide = 0.12
PeelSmallSide = 0.05
PeelStops = 800
PeelRounding = 0.01
PeelEdgeInset = 0.01
)
func NewPeel() model3d.Solid {
mesh := PeelMesh(PeelStops)
return model3d.NewColliderSolidInset(model3d.MeshToCollider(mesh), -PeelRounding)
}
// PeelMesh creates a mesh for the peel.
func PeelMesh(stops int) *model3d.Mesh {
curve := PeelCentralCurve()
twist := PeelTwist()
centralDir := func(x float64) model3d.Coord3D {
delta := 0.001
if x > 0 {
x -= delta
}
return curve(x + delta).Sub(curve(x)).Normalize()
}
corners := func(t int) [4]model3d.Coord3D {
x := float64(t)/float64(stops)*(1-PeelEdgeInset)*2 - (1 - PeelEdgeInset)
c := curve(x)
dir := centralDir(x)
theta := model2d.CurveEvalX(twist, x)
rotation := model3d.Rotation(dir, theta)
longDir := model3d.Z(1.0)
shortDir := longDir.Cross(dir).Normalize()
longDir = rotation.Apply(longDir).Scale(PeelLongSide / 2.0)
shortDir = rotation.Apply(shortDir).Scale(PeelSmallSide / 2.0)
scales := [4][2]float64{{1, 1}, {1, -1}, {-1, -1}, {-1, 1}}
res := [4]model3d.Coord3D{}
for i, scale := range scales {
res[i] = c.Add(shortDir.Scale(scale[0])).Add(longDir.Scale(scale[1]))
}
return res
}
res := model3d.NewMesh()
for t := 0; t < stops; t++ {
corners1 := corners(t)
corners2 := corners(t + 1)
for i := 0; i < 4; i++ {
res.AddQuad(corners1[(i+1)%4], corners1[i], corners2[i], corners2[(i+1)%4])
}
}
for _, t := range [2]int{0, stops} {
corners := corners(t)
if t == 0 {
res.AddQuad(corners[0], corners[1], corners[2], corners[3])
} else {
res.AddQuad(corners[1], corners[0], corners[3], corners[2])
}
}
return res
}
// PeelCentralCurve gets the curve of the peel's center,
// as a parameter of x.
func PeelCentralCurve() func(x float64) model3d.Coord3D {
planeCurve := PeelCurve()
zCurve := PeelHeight()
return func(x float64) model3d.Coord3D {
return model3d.XYZ(x, model2d.CurveEvalX(planeCurve, x), model2d.CurveEvalX(zCurve, x))
}
}
// PeelCurve creates a 2D projection of the overall peel
// on the plane.
func PeelCurve() model2d.Curve {
return model2d.JoinedCurve{
model2d.BezierCurve{
model2d.XY(-1.0, 0.0),
model2d.XY(-0.6, 0.6),
model2d.XY(0.0, 0.0),
},
model2d.BezierCurve{
model2d.XY(0.0, 0.0),
model2d.XY(0.6, -0.6),
model2d.XY(1.0, 0.0),
},
}
}
// PeelHeight creates the z-component of the peel on the
// plane, where x maps to z.
func PeelHeight() model2d.Curve {
return model2d.JoinedCurve{
model2d.BezierCurve{
model2d.XY(-1.0, -0.3),
model2d.XY(-0.2, -0.06),
},
model2d.BezierCurve{
model2d.XY(-0.2, -0.06),
model2d.XY(-0.1, -0.03),
// Provide a small lift above the line.
model2d.XY(0.0, 0.05),
model2d.XY(0.1, -0.03),
model2d.XY(0.2, -0.06),
},
model2d.BezierCurve{
model2d.XY(0.2, -0.06),
model2d.XY(1.0, -0.3),
},
}
}
// PeelTwist creates a function of theta with respect to x.
func PeelTwist() model2d.Curve {
return model2d.JoinedCurve{
model2d.BezierCurve{
model2d.XY(-1.0, 0.0),
model2d.XY(-0.2, 0.0),
},
model2d.BezierCurve{
model2d.XY(-0.2, 0.0),
model2d.XY(-0.05, 0.0),
model2d.XY(0.05, math.Pi),
model2d.XY(0.2, math.Pi),
},
model2d.BezierCurve{
model2d.XY(0.2, math.Pi),
model2d.XY(1.0, math.Pi),
},
}
}