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你现在看到的这片海
This ocean has no

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没有一个三角形，也没有一张贴图
triangles and no textures.

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它完全由 Shader 画出来
It is drawn entirely by a shader:

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一小段运行在 GPU 上的程序
a tiny program on the GPU that computes

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同时为屏幕上的两百万个像素，各算一次颜色
a color for each of two million pixels at once.

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今天从零开始，一步一步写出波浪、黑洞和史瓦西半径
Today we build it step by step: waves, a black hole, the Schwarzschild radius,

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让海水被吸进去，最后迎来一场宇宙大爆炸
water pulled in, and finally a big bang.

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先从最小的 Shader 开始
Start with the smallest shader.

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每个像素都会拿到自己的屏幕坐标
Every pixel gets its own screen coordinate;

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除以分辨率，就得到零到一之间的 UV
divide by the resolution to get a UV between zero and one.

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片元 Shader 只做一件事
A fragment shader does one thing:

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输入坐标，输出颜色
coordinate in, color out.

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把 UV 直接当成红和绿，整块屏幕就变成了渐变
Use UV as red and green, and the whole screen becomes a gradient.

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两百万个像素，同一段代码
Two million pixels, one program,

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同时运行。这就是 GPU 的力量
all at once. That is the power of the GPU.

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接着，用几层正弦波叠出海面
Next, stack a few sine waves into a sea.

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每一层方向和频率都不同
Each layer has its own direction and frequency,

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再用指数函数把波峰压得更尖
and an exponential sharpens the crests.

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高度场有了，做一次有限差分就得到法线
With a height field, one finite difference gives the normal.

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法线决定每个像素朝向哪里，也就决定了光怎么反射
The normal says where each pixel faces, and so how light reflects.

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再加上菲涅尔：视线越贴近水面
Add Fresnel: the lower the view angle,

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海就越像一面镜子，倒映出天空和落日
the more the sea becomes a mirror for the sky and the setting sun.

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现在，在海面上空放一个黑洞。没有模型
Now place a black hole above the sea. No model,

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也没有后期特效，只是让每一条视线在引力里拐弯
no post effect, just every line of sight bending in gravity.

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光线每走一小步，就被拉向黑洞中心；角动量越大
With every small step a ray is pulled toward the center; the more angular momentum,

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拐得越少。迭代几十次，天空和海面就被扭成一圈光环
the less it bends. A few dozen steps twist sky and sea into a ring of light.

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如果光线落进了视界，就再也出不来
If a ray falls inside the horizon it never returns,

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那个像素直接输出纯黑
and that pixel simply outputs black.

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黑洞的大小由史瓦西半径决定
The size of a black hole is set

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它等于二倍的引力常数乘以质量，再除以光速的平方
by the Schwarzschild radius: two G M over c squared.

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红圈是事件视界；一点五倍半径处是光子球
The red ring is the event horizon; at one and a half radii sits the photon sphere,

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光可以绕着黑洞转圈；三倍半径，是最内稳定轨道
where light can orbit; at three radii, the innermost stable orbit.

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质量翻倍，半径就翻倍
Double the mass and the radius doubles.

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把质量交给 Shader 的一个参数
Hand the mass to the shader as one parameter

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我们就能随时让黑洞长大
and we can grow the hole at will.

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再给黑洞加上吸积盘。光线每穿过赤道面一次
Now add an accretion disk. Each time a ray crosses the equatorial plane,

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就采样一圈炽热的气体
it samples a ring of glowing gas.

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内圈转得快、温度高，发白
The inner gas spins fast and runs white-hot;

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外圈转得慢，渐渐变成橙红
the outer gas slows and turns orange.

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朝向我们的一侧，因为多普勒效应更亮
The side moving toward us is brighter thanks to the Doppler effect.

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盘的背面也会被引力折到黑洞上方
Even the far side of the disk is bent over the top of the hole.

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那道弯曲的光弧，就是它
That curved arc of light is it.

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黑洞开始吸水。我们把海面的坐标绕黑洞旋转
The hole starts drinking the sea. We rotate the water coordinates around it,

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越靠近中心转得越快，波浪就卷成了螺旋
faster toward the center, and the waves curl into a spiral.

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同时把水面朝黑洞抬起，形成一根被引力拉起的水柱
We also lift the surface toward the hole, forming a column of water pulled up by gravity,

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泡沫沿着螺旋被甩出去
with foam flung along the spiral.

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这一切，只是改了几行采样坐标
All of it is a few lines changing the sampling coordinates.

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没有粒子系统，也没有流体模拟
No particle system, no fluid simulation.

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接下来，让质量持续增长。史瓦西半径越变越大
Now let the mass keep growing. The Schwarzschild radius swells,

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视界先吞掉海面，再吞掉天空
and the horizon swallows the sea, then the sky.

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光线无处可逃，每一个像素都落进视界
No ray can escape. Every pixel falls inside the horizon,

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屏幕一点一点变成纯黑
and the screen fades to pure black.

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没有海，没有天，也没有光
No sea, no sky, no light.

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然而，奇点无法一直坍缩。一个点，突然爆发
But a singularity cannot collapse forever. A single point suddenly erupts.

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同一个 Shader
Same shader, a new formula:

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换一个公式：密度从中心向外膨胀
density expands outward from the center,

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温度从白热冷却成橙红，再冷却成深蓝
and the temperature cools from white-hot to orange to deep blue.

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无数星点向外飞散，星云开始成形
Countless stars fly outward and nebulae take shape.

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一个新的宇宙，诞生了
A new universe is born.

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回头看，从渐变到海浪，从黑洞到爆炸
Looking back, from gradient to waves, from black hole to explosion,

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我们只写了一个 Shader
we wrote just one shader,

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核心始终是同一个问题：这个像素，应该是什么颜色？
built around one question: what color should this pixel be?

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当你理解了这一点，Shader 就不只是特效
Once you see that, a shader is more than an effect:

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而是一台，可以创造宇宙的机器
it is a machine that can create a universe.