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de.bixilon.kotlinglm.MatrixInterpolation.kt Maven / Gradle / Ivy
package de.bixilon.kotlinglm
import de.bixilon.kotlinglm.GLM.πf
import de.bixilon.kotlinglm.mat4x4.Mat4
import de.bixilon.kotlinglm.vec3.Vec3
import kotlin.math.*
interface MatrixInterpolation {
/** @return angle */
fun axisAngle(mat: Mat4, axis: Vec3): Float {
var angle = 0f
val epsilon = 0.01f
val epsilon2 = 0.1f
if (abs(mat[1, 0] - mat[0, 1]) < epsilon && abs(mat[2, 0] - mat[0, 2]) < epsilon && abs(mat[2, 1] - mat[1, 2]) < epsilon) {
if (abs(mat[1, 0] + mat[0, 1]) < epsilon2 && abs(mat[2, 0] + mat[0, 2]) < epsilon2 && abs(mat[2, 1] + mat[1, 2]) < epsilon2 && abs(mat[0, 0] + mat[1, 1] + mat[2, 2] - 3f) < epsilon2) {
axis.x = 1f
axis.y = 0f
axis.z = 0f
return angle
}
angle = GLM.PIf
val xx = (mat[0, 0] + 1f) * 0.5f
val yy = (mat[1, 1] + 1f) * 0.5f
val zz = (mat[2, 2] + 1f) * 0.5f
val xy = (mat[1, 0] + mat[0, 1]) * 0.25f
val xz = (mat[2, 0] + mat[0, 2]) * 0.25f
val yz = (mat[2, 1] + mat[1, 2]) * 0.25f
when {
xx > yy && xx > zz -> when {
xx < epsilon -> {
axis.x = 0f
axis.y = 0.7071f
axis.z = 0.7071f
}
else -> {
axis.x = sqrt(xx)
axis.y = xy / axis.x
axis.z = xz / axis.x
}
}
yy > zz -> when {
yy < epsilon -> {
axis.x = 0.7071f
axis.y = 0f
axis.z = 0.7071f
}
else -> {
axis.y = sqrt(yy)
axis.x = xy / axis.y
axis.z = yz / axis.y
}
}
else -> when {
zz < epsilon -> {
axis.x = 0.7071f
axis.y = 0.7071f
axis.z = 0f
}
else -> {
axis.z = sqrt(zz)
axis.x = xz / axis.z
axis.y = yz / axis.z
}
}
}
return angle
}
var s = sqrt((mat[2, 1] - mat[1, 2]) * (mat[2, 1] - mat[1, 2]) + (mat[2, 0] - mat[0, 2]) * (mat[2, 0] - mat[0, 2]) + (mat[1, 0] - mat[0, 1]) * (mat[1, 0] - mat[0, 1]))
if (abs(s) < 0.001f)
s = 1f
val angleCos = (mat[0, 0] + mat[1, 1] + mat[2, 2] - 1f) * 0.5f
angle = when {
angleCos - 1f < epsilon -> πf * 0.25f
else -> acos(angleCos)
}
axis.x = (mat[1][2] - mat[2][1]) / s
axis.y = (mat[2][0] - mat[0][2]) / s
axis.z = (mat[0][1] - mat[1][0]) / s
return angle
}
fun axisAngleMatrix(axis: Vec3, angle: Float): Mat4 {
val c = cos(angle)
val s = sin(angle)
val t = 1f - c
val n = axis.normalize()
return Mat4(
t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, 0f,
t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, 0f,
t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, 0f,
0f, 0f, 0f, 1f)
}
fun extractMatrixRotation(m: Mat4) = Mat4(
m[0, 0], m[0, 1], m[0, 2], 0f,
m[1, 0], m[1, 1], m[1, 2], 0f,
m[2, 0], m[2, 1], m[2, 2], 0f,
0f, 0f, 0f, 1f)
fun interpolate(m1: Mat4, m2: Mat4, delta: Float): Mat4 {
val m1rot = extractMatrixRotation(m1)
val dltRotation = m2 * m1rot.transpose()
val dltAxis = Vec3()
val dltAngle = axisAngle(dltRotation, dltAxis)
val out = axisAngleMatrix(dltAxis, dltAngle * delta) * m1rot
out[3, 0] = m1[3, 0] + delta * (m2[3, 0] - m1[3, 0])
out[3, 1] = m1[3, 1] + delta * (m2[3, 1] - m1[3, 1])
out[3, 2] = m1[3, 2] + delta * (m2[3, 2] - m1[3, 2])
return out
}
}
