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Created July 21, 2015 15:07
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Compression algorithm for rotation quaternions (ported from Gaffron Games implementation https://github.com/ThisIsRobokitty/netgame/blob/60ac89873a53b02611a88b0d5b10987d4693a9ad/XX%20-%20Fiedler's%20Cubes/Engine.h)
using System;
using UnityEngine;
namespace RamjetAnvil.Networking {
public static class Compression {
public static class Rotation {
private const float Minimum = -1.0f / 1.414214f; // note: 1.0f / sqrt(2)
private const float Maximum = +1.0f / 1.414214f;
public static uint Compress(Quaternion rotation) {
float absX = Mathf.Abs(rotation.x),
absY = Mathf.Abs(rotation.y),
absZ = Mathf.Abs(rotation.z),
absW = Mathf.Abs(rotation.w);
var largestComponent = new LargestComponent(ComponentType.X, absX);
if (absY > largestComponent.Value) {
largestComponent.Value = absY;
largestComponent.ComponentType = ComponentType.Y;
}
if (absZ > largestComponent.Value) {
largestComponent.Value = absZ;
largestComponent.ComponentType = ComponentType.Z;
}
if (absW > largestComponent.Value) {
largestComponent.Value = absW;
largestComponent.ComponentType = ComponentType.W;
}
float a, b, c;
switch (largestComponent.ComponentType) {
case ComponentType.X:
if (rotation.x >= 0) {
a = rotation.y;
b = rotation.z;
c = rotation.w;
} else {
a = -rotation.y;
b = -rotation.z;
c = -rotation.w;
}
break;
case ComponentType.Y:
if (rotation.y >= 0) {
a = rotation.x;
b = rotation.z;
c = rotation.w;
} else {
a = -rotation.x;
b = -rotation.z;
c = -rotation.w;
}
break;
case ComponentType.Z:
if (rotation.z >= 0) {
a = rotation.x;
b = rotation.y;
c = rotation.w;
} else {
a = -rotation.x;
b = -rotation.y;
c = -rotation.w;
}
break;
case ComponentType.W:
if (rotation.w >= 0) {
a = rotation.x;
b = rotation.y;
c = rotation.z;
} else {
a = -rotation.x;
b = -rotation.y;
c = -rotation.z;
}
break;
default:
// Should never happen!
throw new ArgumentOutOfRangeException("Unknown rotation component type: " +
largestComponent.ComponentType);
}
float normalizedA = (a - Minimum) / (Maximum - Minimum),
normalizedB = (b - Minimum) / (Maximum - Minimum),
normalizedC = (c - Minimum) / (Maximum - Minimum);
uint integerA = (uint) Mathf.FloorToInt(normalizedA * 1024.0f + 0.5f),
integerB = (uint) Mathf.FloorToInt(normalizedB * 1024.0f + 0.5f),
integerC = (uint) Mathf.FloorToInt(normalizedC * 1024.0f + 0.5f);
return (((uint) largestComponent.ComponentType) << 30) | (integerA << 20) | (integerB << 10) | integerC;
}
public static Quaternion Decompress(uint compressedRotation) {
var largestComponentType = (ComponentType) (compressedRotation >> 30);
uint integerA = (compressedRotation >> 20) & ((1 << 10) - 1),
integerB = (compressedRotation >> 10) & ((1 << 10) - 1),
integerC = compressedRotation & ((1 << 10) - 1);
float a = integerA / 1024.0f * (Maximum - Minimum) + Minimum,
b = integerB / 1024.0f * (Maximum - Minimum) + Minimum,
c = integerC / 1024.0f * (Maximum - Minimum) + Minimum;
Quaternion rotation;
switch (largestComponentType) {
case ComponentType.X:
// (?) y z w
rotation.y = a;
rotation.z = b;
rotation.w = c;
rotation.x = Mathf.Sqrt(1 - rotation.y * rotation.y
- rotation.z * rotation.z
- rotation.w * rotation.w);
break;
case ComponentType.Y:
// x (?) z w
rotation.x = a;
rotation.z = b;
rotation.w = c;
rotation.y = Mathf.Sqrt(1 - rotation.x * rotation.x
- rotation.z * rotation.z
- rotation.w * rotation.w);
break;
case ComponentType.Z:
// x y (?) w
rotation.x = a;
rotation.y = b;
rotation.w = c;
rotation.z = Mathf.Sqrt(1 - rotation.x * rotation.x
- rotation.y * rotation.y
- rotation.w * rotation.w);
break;
case ComponentType.W:
// x y z (?)
rotation.x = a;
rotation.y = b;
rotation.z = c;
rotation.w = Mathf.Sqrt(1 - rotation.x * rotation.x
- rotation.y * rotation.y
- rotation.z * rotation.z);
break;
default:
// Should never happen!
throw new ArgumentOutOfRangeException("Unknown rotation component type: " +
largestComponentType);
}
return rotation;
}
private enum ComponentType : uint {
X = 0,
Y = 1,
Z = 2,
W = 3
}
private struct LargestComponent {
public ComponentType ComponentType;
public float Value;
public LargestComponent(ComponentType componentType, float value) {
ComponentType = componentType;
Value = value;
}
}
}
}
}
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