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tube.go
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tube.go
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// Copyright 2016 The G3N Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// TODO: UVs, Caps
package geometry
import (
"math"
"github.com/g3n/engine/gls"
"github.com/g3n/engine/math32"
)
func CalculateNormals(indices math32.ArrayU32, positions, normals math32.ArrayF32) math32.ArrayF32 {
var x1x2, y1y2, z1z2, x3x2, y3y2, z3z2, x, y, z, l float32
var x1, y1, z1, x2, y2, z2, x3, y3, z3 int // position indexes
for i := 0; i < len(indices)/3; i++ {
x1 = int(indices[i*3] * uint32(3))
y1 = x1 + 1
z1 = x1 + 2
x2 = int(indices[i*3+1] * uint32(3))
y2 = x2 + 1
z2 = x2 + 2
x3 = int(indices[i*3+2] * uint32(3))
y3 = x3 + 1
z3 = x3 + 2
x1x2 = positions[x1] - positions[x2]
y1y2 = positions[y1] - positions[y2]
z1z2 = positions[z1] - positions[z2]
x3x2 = positions[x3] - positions[x2]
y3y2 = positions[y3] - positions[y2]
z3z2 = positions[z3] - positions[z2]
x = y1y2*z3z2 - z1z2*y3y2
y = z1z2*x3x2 - x1x2*z3z2
z = x1x2*y3y2 - y1y2*x3x2
l = float32(math.Sqrt(float64(x)*float64(x) + float64(y)*float64(y) + float64(z)*float64(z)))
if l == 0 {
l = 1.0
}
normals[x1] += x / l
normals[y1] += y / l
normals[z1] += z / l
normals[x2] += x / l
normals[y2] += y / l
normals[z2] += z / l
normals[x3] += x / l
normals[y3] += y / l
normals[z3] += z / l
}
for i := 0; i < len(normals)/3; i++ {
x = normals[i*3]
y = normals[i*3+1]
z = normals[i*3+2]
l = float32(math.Sqrt(float64(x)*float64(x) + float64(y)*float64(y) + float64(z)*float64(z)))
if l == 0 {
l = 1.0
}
normals[i*3] = x / l
normals[i*3+1] = y / l
normals[i*3+2] = z / l
}
return normals
}
func NewRibbon(paths [][]math32.Vector3, close bool) *Geometry {
/*
if len(paths) < 3 {
close = false
}
*/
c := NewGeometry()
var ls, is []int // path lengths, path indexes
positions := math32.NewArrayF32(0, 0)
indices := math32.NewArrayU32(0, 0)
i := 0
for p := 0; p < len(paths); p++ {
path := paths[p]
l := len(path)
ls = append(ls, l)
is = append(is, i)
for j := 0; j < l; j++ {
positions.AppendVector3(&path[j])
}
i += l
}
l1 := ls[0] - 1 // path1 length
l2 := ls[1] - 1 // path2 length
min := l2
if l1 < l2 {
min = l1
}
p := 0
i = 0
for i <= min && p < len(ls)-1 {
t := is[p+1] - is[p]
indices.Append(uint32(i), uint32(i+t), uint32(i+1))
indices.Append(uint32(i+t+1), uint32(i+1), uint32(i+t))
i++
if i == min {
if close {
indices.Append(uint32(i), uint32(i+t), uint32(is[p]))
indices.Append(uint32(is[p]+t), uint32(is[p]), uint32(i+t))
}
p++
if p == len(ls)-1 {
break
}
l1 = ls[p] - 1
l2 = ls[p+1] - 1
i = is[p]
if l1 < l2 {
min = l1 + i
} else {
min = l2 + i
}
}
}
normals := math32.NewArrayF32(positions.Size(), positions.Size())
normals = CalculateNormals(indices, positions, normals)
c.SetIndices(indices)
c.AddVBO(gls.NewVBO(positions).AddAttrib(gls.VertexPosition))
c.AddVBO(gls.NewVBO(normals).AddAttrib(gls.VertexNormal))
return c
}
func NewTube(path []math32.Vector3, radius float32, radialSegments int, close bool) *Geometry {
l := len(path)
var tangents, normals, binormals []math32.Vector3
tangents = make([]math32.Vector3, l)
normals = make([]math32.Vector3, l)
binormals = make([]math32.Vector3, l)
tangents[0] = *path[1].Clone().Sub(&path[0])
tangents[0].Normalize()
tangents[l-1] = *path[l-1].Clone().Sub(&path[l-2])
tangents[l-1].Normalize()
var tmpVertex *math32.Vector3
if tangents[0].X != 1 {
tmpVertex = math32.NewVector3(1, 0, 0)
} else if tangents[0].Y != 1 {
tmpVertex = math32.NewVector3(0, 1, 0)
} else if tangents[0].Z != 1 {
tmpVertex = math32.NewVector3(0, 0, 1)
}
normals[0] = *tangents[0].Clone().Cross(tmpVertex)
normals[0].Normalize()
binormals[0] = *tangents[0].Clone().Cross(&normals[0])
binormals[0].Normalize()
for i := 1; i < l; i++ {
prev := *path[i].Clone().Sub(&path[i-1])
if i < l-1 {
cur := *path[i+1].Clone().Sub(&path[i])
tangents[i] = *prev.Clone().Add(&cur)
tangents[i].Normalize()
}
normals[i] = *binormals[i-1].Clone().Cross(&tangents[i])
normals[i].Normalize()
binormals[i] = *tangents[i].Clone().Cross(&normals[i])
binormals[i].Normalize()
}
pi2 := math.Pi * 2
step := pi2 / float64(radialSegments)
var radialPaths [][]math32.Vector3
for i := 0; i < l; i++ {
var radialPath []math32.Vector3
var ang float32
for ang = 0.0; ang < float32(pi2); ang += float32(step) {
matrix := math32.NewMatrix4()
matrix.MakeRotationAxis(&tangents[i], ang)
x := normals[i].X
y := normals[i].Y
z := normals[i].Z
rw := 1 / (x*matrix[3] + y*matrix[7] + z*matrix[11] + matrix[15])
newX := (x*matrix[0] + y*matrix[4] + z*matrix[8] + matrix[12]) * rw
newY := (x*matrix[1] + y*matrix[5] + z*matrix[9] + matrix[13]) * rw
newZ := (x*matrix[2] + y*matrix[6] + z*matrix[10] + matrix[14]) * rw
rotated := math32.NewVector3(newX, newY, newZ).MultiplyScalar(radius).Add(&path[i])
radialPath = append(radialPath, *rotated)
}
radialPaths = append(radialPaths, radialPath)
}
return NewRibbon(radialPaths, close)
}