2021.06.20

• dx spherical mapping 有一条虚线
• off-screen alpha blend

dx spherical mapping 有一条虚线

类似于这种, 虚线 seam have a thickness of 2 pixels
https://stackoverflow.com/questions/19723698/sphere-texture-mapping-error

• mipmap calculation
  https://forum.unity.com/threads/calculate-used-mipmap-level-ddx-ddy.255237/
  mip map level 是根据相邻两个像素的uv梯度来决定的, spherical mapping在接缝处会从0跃变到1, 就会使用最大的mip map level, 把lod强制设置为0可以解决这个问题。

  float mip_map_level(in float2 texture_coordinate) // in texel units
{
  float2  dx_vtc  = ddx(texture_coordinate);
  float2  dy_vtc  = ddy(texture_coordinate);
  float delta_max_sqr = max(dot(dx_vtc, dx_vtc), dot(dy_vtc, dy_vtc));
  return 0.5 * log2(delta_max_sqr);
}
(x,y)->(u1,v1) 这里的u, v不是归一化的uv, 是乘以resolution之后的u, v
(x+1, y)->(u2,v2)
ddx(x,y) = (u2-u1, v2-v1)
(x,y)->(u1,v1)
(x, y+1)->(u2,v2)
ddy(x, y) = (u2-u1, v2-v1)
 sqrt(deltau * deltau + deltav * deltav) = k, 
 when k = 1 -> 1 screen pixel = 1 texel pixel, log2(k) = 0, this level 0, 
 when k = 2, 1 screen pixel = 2 pixel, log2(k) = 1, and so on. 
 set log2(k) = q, 2^q = k -> 2^q * 2^q = k * k -> 2^(2q) = k*k
-> log2(k*k) = 2q -> q = 0.5 * log2(k*k) -> q = 0.5 * log2(deltau * deltau + deltav * deltav)

off-screen alpha blend

https://developer.nvidia.com/gpugems/gpugems3/part-iv-image-effects/chapter-23-high-speed-screen-particles
最近遇到大气，云，还有粒子的alpha blend要好好想想，否则即使效果上没有什么太大问题，但从理论上来说是不正确的，能量上可能是不守恒的。