Nonlinear Falloff in Houdini VEX: Smoothing Point Positions by Step Index

When building procedural models, chain rigs, or edge flattening setups in Houdini, you frequently need to ease points toward a base target position along a sequence of topological steps.

While a basic fit() gives you a linear transition, linear falloffs often look mechanical and rigid. Applying an exponential curve via pow()—or controlling it via a spline ramp—gives you full artistic control over the blending tension.

Here is an optimized Point Wrangle SOP implementation for pulling point positions along a step gradient, how the exponent math behaves, and a visual ramp alternative.

The VEX Snippet: Exponential Falloff

This snippet looks up a base reference point marked with i@step == 0, extracts its Z coordinate, and smoothly blends downstream points (i@step >= 1) toward that target height using an exponential curve.

// Run over: Points
int max_steps = chi("max_steps");
float exp = chf("exponent"); 

// Locate the reference point carrying step == 0
int base_pt = findattribval(0, "point", "step", 0);

if (base_pt >= 0) {
    vector base_pos = point(0, "P", base_pt);
    float target_z = base_pos.z;
    
    int s = i@step;
    
    if (s >= 1 && s <= max_steps) {
        // Linear normalized falloff from 1.0 (at step 1) down to 0.0 (at max_steps)
        float linear_strength = fit(s, 1, max_steps, 1.0, 0.0);
        
        // Shape the curve using an exponential power:
        // exp == 1.0 -> Linear falloff
        // exp > 1.0  -> Steep/fast drop-off near step 1 (aggressive initial decay)
        // exp < 1.0  -> Slow drop-off (retains strength longer before trailing off)
        float strength = pow(clamp(linear_strength, 0.0, 1.0), exp);
        
        // Blend current Z position toward target Z
        @P.z = lerp(@P.z, target_z, strength);
    }
}

Performance Tip: findattribval() performs a search across your point cache. If you are executing this over tens of thousands of points, consider querying base_pos once in a Detail Wrangle and passing it downstream, or ensure your attribute is indexed.

Understanding the Math: How pow() Shapes Normalized Values

Because linear_strength falls strictly between 0.0 and 1.0, raising it to powers behaves differently than with numbers greater than 1:

Strength (1.0)
  ▲
1 │───\           exp = 0.5 (Holds strength longer)
  │    \──\
  │     \   \     exp = 1.0 (Linear)
  │      \    \
  │       \    \  exp = 2.0 (Fast initial decay)
0 └───────┴─────┴────────► Steps (1 to max_steps)

Alternative: Visual Control Using chramp()

If tweaking decimal exponents in a numeric field feels too abstract, swap the math for a Ramp Parameter. This gives you an interactive Bézier/Spline curve editor directly on the SOP interface:

// Run over: Points
int max_steps = chi("max_steps");
int base_pt = findattribval(0, "point", "step", 0);

if (base_pt >= 0) {
    float target_z = point(0, "P", base_pt).z;
    int s = i@step;
    
    if (s >= 1 && s <= max_steps) {
        // Map step progression from 0.0 (near) to 1.0 (far)
        float u = fit(s, 1, max_steps, 0.0, 1.0);
        
        // Sample visual curve editor in the UI
        float strength = chramp("falloff_curve", u);
        
        @P.z = lerp(@P.z, target_z, strength);
    }
}

After pasting this, click the Create Spare Parameters button on the top right of the Point Wrangle node. You will get a draggable spline curve where the left side ($u=0$) defines the influence at step 1 and the right side ($u=1$) defines the tail influence at max_steps.