Unity 学习笔记：Signed Distance Field 8SSEDT 算法
Signed Distance Field (有向距离场) 技术在如今的图形渲染项目中有着广泛的运用，例如 Ray Marching、风格化卡通渲染的人物面部光照等等， 如果我们想在线性的时间内，通过一张二值化的黑白图，生成一张 SDF 图，那么目前 8SSEDT (8-points Signed Sequential Euclidean Distance Transform) 算法是比较流行的解法。8SSEDT 的核心就是递推算法——把复杂问题拆解成连续的简单问题。SDF 图记录的是当前像素到物体的距离，距离是连续的，也就是说我们可以通过临近像素的距离推到出当前像素的距离。
核心思路：
假设有一张黑白原图，观察其 9 个点的局部，其每个点的平方距离如下
Raw Data Sqr Dist
[ 2][ 1][ 1]
[ 1][ 0][ 0]
[ 1][ 0][-1]首先遍历一遍黑白原图，建立一个像素网格数据，标记出原图的黑白部分，白色像素标记距离0，黑色像素标记为一个尽可能的最大值，这组网格数据用于推到向外的距离场。再建立一个像素网格数据，反向标记，黑色像素标记距离0，白色像素标记为一个尽可能的最大值，用于推导向内的距离场。
#Data1 #Data2
[∞][∞][∞]
[∞] [∞][∞]
[∞] [∞][∞]推导过程则是一个像素分别和周边的 8 个像素进行比较
[#8][#7][#6]
[#1][ 0][#5]
[#2][#3][#4]unity 图像的的 UV 坐标的是从左下到右上的，针对第一组向外的网格数据，首先我们可以从左往右、从下到上推，对比当前像素到左边、左下，下边像素的距离。然后再从右往左、从下到上推，对比当前像素到右下、右边像素的距离
^ [ ][ ][ ] ^ [ ][ ][ ]
| [?][ ] | [ ][?]
| [?][?][ ] | [ ][ ][?]
- - - > < - - - 再反方向和另外一边的像素再比较推导一遍，这样 8 个像素就无死角的比较完了。
< - - - - - - >
[ ][?][?] | [?][ ][ ] |
[ ][?] | [?][ ] |
[ ][ ][ ] v [ ][ ][ ] v对第二组向内的网格数据重复上面的推导。最后两个合格数据合并在一起就可以得到完整的有向距离场了。
关于SDF贴图的颜色和尺寸的一些想法
已知通常最后是要把 SDF 信息存储到单通道 8 位的贴图上的，也就是说可用的黑白色阶只有 0~255 个，我们最后需要把距离换算到 256 的区间比例里，也就是说在记录距离上，不管你的贴图尺寸多大，其距离信息基本和长宽 256 的贴图等效，所以 SDF 贴图对尺寸并不敏感。在后期的贴图压缩上，可以选择对尺寸进行压缩，但最好不要对精度进行压缩。
最后是 8SSEDT 在 Unity 里实现的核心代码:
using UnityEngine;
using static UnityEngine.Mathf;
public class SDFGeneratorCore
{
private const int MaxDistance = 2147483647;
private enum Type
{
Object,
Empty,
}
private struct Pixel
{
public Type type;
public int dx, dy;
public int sqrDistance;
public Pixel(Type type, int dx, int dy)
{
this.type = type;
this.dx = dx;
this.dy = dy;
sqrDistance = dx * dx + dy * dy;
}
public Pixel(Type type, int dx, int dy, int sqrDistance)
{
this.type = type;
this.dx = dx;
this.dy = dy;
this.sqrDistance = sqrDistance;
}
}
private struct TexData
{
private int sizeX,sizeY;
public Pixel[,] pixels;
public TexData(int x, int y)
{
pixels = new Pixel;
sizeX = x - 1;
sizeY = y - 1;
}
public Pixel GetPixel(int x, int y)
{
if (x < 0 || x > sizeX || y < 0 || y > sizeY)
return new Pixel(Type.Empty, 0, 0, MaxDistance);
else
return pixels;
}
}
public Texture2D CreateSDFTex(Texture2D rawTex)
{
int width = rawTex.width;
int height = rawTex.height;
TexData whiteSideData = new TexData(width, height);
TexData blackSideData = new TexData(width, height);
MarkRawData(ref whiteSideData, ref blackSideData, rawTex, width, height);
GenerateSDF(ref whiteSideData, ref blackSideData, width, height);
Texture2D newTex = new Texture2D(width, height);
WriteTex(newTex, whiteSideData, blackSideData, width, height);
return newTex;
}
void MarkRawData(ref TexData whiteSideData, ref TexData blackSideData, Texture2D tex, int width, int height)
{
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
int value = (int)tex.GetPixel(x, y).r;
if (value == 1)
{
whiteSideData.pixels = new Pixel(Type.Object, 0, 0, 0);
blackSideData.pixels = new Pixel(Type.Empty, 0, 0, MaxDistance);
}
else
{
whiteSideData.pixels = new Pixel(Type.Empty, 0, 0, MaxDistance);
blackSideData.pixels = new Pixel(Type.Object, 0, 0, 0);
}
}
}
}
void ComparePixel(ref TexData data, int x, int y, int offsetX, int offsetY)
{
Pixel other = data.GetPixel(x + offsetX, y + offsetY);
if (other.sqrDistance == MaxDistance || other.sqrDistance >= data.pixels.sqrDistance)
return;
Pixel tmp = new Pixel(Type.Empty,other.dx + Abs(offsetX),other.dy + Abs(offsetY));
if (data.pixels.sqrDistance > tmp.sqrDistance)
{
data.pixels = tmp;
}
}
void ComparePixels(ref TexData data, int x, int y, int ox0, int oy0, int ox1, int oy1)
{
ComparePixel(ref data, x, y, ox0, oy0);
ComparePixel(ref data, x, y, ox1, oy1);
}
void ComparePixels(ref TexData data, int x, int y, int ox0, int oy0, int ox1, int oy1, int ox2, int oy2)
{
ComparePixel(ref data, x, y, ox0, oy0);
ComparePixel(ref data, x, y, ox1, oy1);
ComparePixel(ref data, x, y, ox2, oy2);
}
void GenerateSDF(ref TexData whiteSideData, ref TexData blackSideData, int width, int height)
{
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
if (whiteSideData.pixels.type != Type.Object)
ComparePixels(ref whiteSideData, x, y, -1, 0, -1, -1, 0, -1);
else
ComparePixels(ref blackSideData, x, y, -1, 0, -1, -1, 0, -1);
}
for (int x = width-1; x >= 0 ; x--)
{
if (whiteSideData.pixels.type != Type.Object)
ComparePixels(ref whiteSideData, x, y, 1, -1, 1, 0);
else
ComparePixels(ref blackSideData, x, y, 1, -1, 1, 0);
}
}
for (int y = height-1; y >= 0 ; y--)
{
for (int x = width-1; x >= 0 ; x--)
{
if (whiteSideData.pixels.type != Type.Object)
ComparePixels(ref whiteSideData, x, y, 1, 0, 1, 1, 0, 1);
else
ComparePixels(ref blackSideData, x, y, 1, 0, 1, 1, 0, 1);
}
for (int x = 0; x < width; x++)
{
if (whiteSideData.pixels.type != Type.Object)
ComparePixels(ref whiteSideData, x, y, -1, 1, -1, 0);
else
ComparePixels(ref blackSideData, x, y, -1, 1, -1, 0);
}
}
}
void WriteTex(Texture2D texture, TexData whiteSideDate, TexData blackSideData, int width, int height)
{
float scale = height / 256f;
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
float value1 = Sqrt(whiteSideDate.pixels.sqrDistance) / scale;
float value2 = Sqrt(blackSideData.pixels.sqrDistance) / scale;
float v = (value1 - value2 + 128f) / 256f;
Color color = new Color(v, v, v);
texture.SetPixel(x,y,color);
}
}
}
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