Let's break this down clearly—first how pow() works in GLSL, then exactly how it shapes the lines in your shader code.

1. GLSL pow() Basics #

At its core, GLSL's pow(base, exponent) does exactly what you'd expect from high school math: it calculates base raised to the power of exponent. A few key details to keep in mind:

• It works with floating-point numbers (both float and vector types—if you pass a vec2/vec3, it computes the power per component).
• Edge cases to watch for:
  • If base is 0.0, exponent can't be negative (that would be division by zero, resulting in undefined behavior).
  • If base is negative, exponent must be an integer (non-integer exponents of negative numbers are complex, which GLSL doesn't handle by default).
• Examples to ground this:
  • pow(2.0, 3.0) → 8.0
  • pow(4.0, 0.5) → 2.0 (this is identical to taking the square root)
  • pow(0.5, 2.0) → 0.25
  • pow(st.x, 5.0) → computes each x-coordinate in your shader's 0-1 coordinate system raised to the 5th power.

2. How pow() Changes Your Plot Lines #

Your plot() function uses smoothstep to draw a smooth, 0.04-unit wide line along the curve defined by pct (which I assume is pow(st.x, some_value) in your full code). Here's how different exponents warp that curve:

When exponent > 1 (e.g., pow(st.x, 2.0), pow(st.x, 5.0)) #

• The curve starts flat near st.x = 0 and gets steeper as st.x approaches 1.
• Visually, your plot line will be low and slow to rise on the left side of the screen, then shoot up sharply on the right. Think of a parabola opening upwards, squashed into the 0-1 range.

When exponent = 1 (e.g., pow(st.x, 1.0)) #

• This simplifies to y = st.x—a straight diagonal line. Your plot will be a perfect 45-degree line across the screen, since every x maps directly to the same y.

When 0 < exponent < 1 (e.g., pow(st.x, 0.5), pow(st.x, 0.2)) #

• The curve rises steeply near st.x = 0 and flattens out as st.x approaches 1.
• Your plot line will jump up quickly on the left, then level off towards the top-right corner. This is the inverse of the exponent >1 case—like a square root curve.

Bonus: Negative Exponents (Less Common in This Context) #

• A negative exponent flips the calculation to 1.0 / pow(base, abs(exponent)). For example, pow(st.x, -2.0) equals 1.0 / (st.x * st.x).
• This causes the value to skyrocket as st.x approaches 0 (since you're dividing by a tiny number), leading to a line that shoots off the top of the screen on the left. You'd typically add a small offset (like st.x + 0.001) to avoid division by zero.

3. Putting It All Together with Your Plot Function #

Your plot() function creates a smooth line by:

1. Using smoothstep(pct-0.02, pct, st.y) to fade in the line from pct-0.02 to pct (the bottom edge of the line).
2. Subtracting smoothstep(pct, pct+0.02, st.y) to fade out the line from pct to pct+0.02 (the top edge of the line).

When pct is set to pow(st.x, exp), the entire line follows the shape of that power curve. Changing the exponent is like bending the diagonal line either up, down, or keeping it straight—all depending on whether the exponent is below 1, above 1, or exactly 1.

内容的提问来源于stack exchange，提问作者Harpreet