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vector4.go
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vector4.go
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package main
import (
"math"
)
type TexVector struct {
u, v, w float64
}
func NewTexVector(u, v, w float64) TexVector {
return TexVector{u, v, w}
}
type Vector4 struct {
x, y, z, w float64
originalZ float64
texVec TexVector
}
func (v1 Vector4) Add(v2 Vector4) Vector4 {
return Vector4{
v1.x + v2.x,
v1.y + v2.y,
v1.z + v2.z,
1,
v1.originalZ + v2.originalZ,
NewTexVector(
v1.texVec.u+v2.texVec.v,
v1.texVec.v+v2.texVec.v,
v1.texVec.w+v2.texVec.w,
),
}
}
func (v1 Vector4) Sub(v2 Vector4) Vector4 {
return Vector4{
v1.x - v2.x,
v1.y - v2.y,
v1.z - v2.z,
1,
v1.originalZ - v2.originalZ,
NewTexVector(
v1.texVec.u-v2.texVec.v,
v1.texVec.v-v2.texVec.v,
v1.texVec.w-v2.texVec.w,
),
}
}
func (v Vector4) Mul(k float64) Vector4 {
return Vector4{
v.x * k,
v.y * k,
v.z * k,
1,
v.originalZ * k,
NewTexVector(
v.texVec.u,
v.texVec.v,
v.texVec.w,
),
}
}
func (v Vector4) Div(k float64) Vector4 {
return Vector4{
v.x / k,
v.y / k,
v.z / k,
1,
v.originalZ / k,
NewTexVector(
v.texVec.u,
v.texVec.v,
v.texVec.w,
),
}
}
func (v1 Vector4) Dot(v2 Vector4) float64 {
return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z
}
func (v Vector4) Len() float64 {
return math.Sqrt(v.Dot(v))
}
func (v Vector4) Normalise() Vector4 {
l := v.Len()
return Vector4{
v.x / l,
v.y / l,
v.z / l,
1,
v.originalZ,
NewTexVector(
v.texVec.u,
v.texVec.v,
v.texVec.w,
),
}
}
func (v1 Vector4) CrossProduct(v2 Vector4) Vector4 {
return Vector4{
v1.y*v2.z - v1.z*v2.y,
v1.z*v2.x - v1.x*v2.z,
v1.x*v2.y - v1.y*v2.x,
1,
v1.originalZ,
NewTexVector(
v1.texVec.u,
v1.texVec.v,
v1.texVec.w,
),
}
}
func IntersectPlane(plane_p, plane_n, lineStart, lineEnd Vector4) Vector4 {
planeN := plane_n.Normalise()
planeD := -planeN.Dot(plane_p)
ad := lineStart.Dot(planeN)
bd := lineEnd.Dot(planeN)
t := (-planeD - ad) / (bd - ad)
lineStartToEnd := lineEnd.Sub(lineStart)
lineToIntersect := lineStartToEnd.Mul(t)
return lineStart.Add(lineToIntersect)
}
func ClipAgainstPlane(plane_p, plane_n Vector4, in_tri Triangle) []Triangle {
planeN := plane_n.Normalise()
dist := func(p Vector4) float64 {
return planeN.x*p.x + planeN.y*p.y + planeN.z*p.z - planeN.Dot(plane_p)
}
var insidePoints, outsidePoints [3]Vector4
nInsidePointCount, nOutsidePointCount := 0, 0
for i := 0; i < 3; i++ {
distance := dist(in_tri.vecs[i])
if distance >= 0 {
insidePoints[nInsidePointCount] = in_tri.vecs[i]
nInsidePointCount++
} else {
outsidePoints[nOutsidePointCount] = in_tri.vecs[i]
nOutsidePointCount++
}
}
// The entire triangle is outside of view. No need to draw it.
if nInsidePointCount == 0 {
return make([]Triangle, 0)
}
// The entire triangle is completly inside of view. Draw it as is.
if nInsidePointCount == 3 {
return []Triangle{in_tri}
}
v0 := &in_tri.vecs[0]
v1 := &in_tri.vecs[1]
v2 := &in_tri.vecs[2]
area := EdgeCross(v0, v1, v2)
updateVector := func(v *Vector4) {
_, alpha, beta, gamma := BaycentricPointInTriangle(area, v0, v1, v2, v)
InterpolateVectors(alpha, beta, gamma, v0, v1, v2, v)
}
// Two points of the triangle are outside of view. Clip it into a new triangle.
if nInsidePointCount == 1 && nOutsidePointCount == 2 {
p1 := IntersectPlane(plane_p, planeN, insidePoints[0], outsidePoints[0])
p2 := IntersectPlane(plane_p, planeN, insidePoints[0], outsidePoints[1])
updateVector(&p1)
updateVector(&p2)
outTri := Triangle{
vecs: [3]Vector4{
insidePoints[0],
p1,
p2,
},
ilum: in_tri.ilum,
tex: in_tri.tex,
}
return []Triangle{outTri}
}
// One point of the triangle is outside of view. Clip triangle into a quad (two triangles).
if nInsidePointCount == 2 && nOutsidePointCount == 1 {
p1 := IntersectPlane(plane_p, planeN, insidePoints[0], outsidePoints[0])
updateVector(&p1)
outTri1 := Triangle{
vecs: [3]Vector4{
insidePoints[0],
insidePoints[1],
p1,
},
ilum: in_tri.ilum,
tex: in_tri.tex,
}
p2 := IntersectPlane(plane_p, planeN, insidePoints[1], outsidePoints[0])
updateVector(&p2)
outTri2 := Triangle{
vecs: [3]Vector4{
insidePoints[1],
outTri1.vecs[2],
p2,
},
ilum: in_tri.ilum,
tex: in_tri.tex,
}
return []Triangle{outTri1, outTri2}
}
return make([]Triangle, 0)
}