Vector Displacement

Arnold allows shaders to displace vertices in a polymesh node. The vertices are displaced in the direction and magnitude of the vector returned by the shader.

In this example shader, we compute a nonlinear displacement based on a noise function. This can displace along the normal of a surface like a traditional noise displacement shader, but it also has the option of blooming out the peaks and valleys of the displacement.

This is done by computing a noise function and its delta in the direction of two surface derivatives. This delta determines the amount the derivatives would be deflected by the displacement. By repeatedly deflecting the derivatives, we create a non-linear displacement that arcs out from the surface. This is equivalent to displacing the surface, computing the normal, and displacing again repeatedly.

Source Code

```/*
*/
#include <ai.h>
#include <string.h>

enum
{
p_octaves,
p_freq,
p_amplitude,
p_bloom,
p_type
};

#define ENUM_SCALAR_TYPES { "perlin", "abs_perlin", "recursive", "abs_recursive", NULL };
#define PERLIN        0
#define ABS_PERLIN    1
#define RECURSIVE     2
#define ABS_RECURSIVE 3
const char *types_enum[] = ENUM_SCALAR_TYPES;

node_parameters
{
AiParameterInt ("octaves"  , 3);
AiParameterFlt ("freq"     , 1);
AiParameterFlt ("amplitude", 1);
AiParameterFlt ("bloom"    , 1);
AiParameterEnum("type"     , PERLIN, types_enum);
}

float scalarfunc(AtVector P, int type, int octaves)
{
float doubler = 1;
float NzAccum = 0;

switch (type)
{
case PERLIN:
return AiPerlin3(P);
case ABS_PERLIN:
return fabs(AiPerlin3(P));
case RECURSIVE:
for (int i = 0; i < octaves; i++) {
NzAccum += AiPerlin3(P*doubler) / doubler;
doubler *= 2;
}
return NzAccum;
case ABS_RECURSIVE:
for (int i = 0; i < octaves; i++) {
NzAccum += fabs(AiPerlin3(P*doubler)) / doubler;
doubler *= 2;
}
return NzAccum;
}

return AiPerlin3(P);
}

{
AtVector Ploc, Uloc, Vloc; // noise sample location, and over in U and V locations
float Np, Nu, Nv;         // noise at P, noise at location over in U and V
float Udelt, Vdelt;       // delta in the noise over in U and V
float delta = .01;        // distance delta for noise samples

AtVector U, V;
if (sg->dPdu != AI_V3_ZERO && sg->dPdv != AI_V3_ZERO)
{
// tangents available, use them
U = sg->dPdu;
V = sg->dPdv;
}
else
{
// no tangents given, compute a pair
AiV3BuildLocalFramePolar(U, V, sg->N);
}

if (type > ABS_PERLIN)
{
// adjust delta to highest frequency in recursive noise
delta *= pow(.5,  octaves) * 2;
}
Ploc = sg->Po * freq;
Uloc = Ploc + U * delta;
Vloc = Ploc + V * delta;

// noise sampled at P, and over in U and V
Np = scalarfunc(Ploc, type, octaves);
Nu = scalarfunc(Uloc, type, octaves);
Nv = scalarfunc(Vloc, type, octaves);

Udelt = (Nu - Np) * bloom;
Vdelt = (Nv - Np) * bloom;

AtVector Pstepped = sg->P;
int steps = 10;
float stepscale = amplitude / steps;

for (int i = 0; i < steps; i++)
{
// stepdir is the cross product of the derivatives
AtVector stepdir = AiV3Cross(U,V);
// deflect the derivatives
U = AiV3Normalize(U + (stepdir * Udelt * stepscale));
V = AiV3Normalize(V + (stepdir * Vdelt * stepscale));
Pstepped += stepdir * Np * stepscale;
}

sg->out.VEC() = Pstepped - sg->P;
}

node_initialize
{
}

node_update
{
}

node_finish
{
}

{
if (i > 0) return false;

node->methods      = NonlinNzMethods;
node->output_type  = AI_TYPE_VECTOR;
node->name         = "nonlinear_noise";
strcpy(node->version, AI_VERSION);
return true;
}```

And here is the .ass file that uses this shader:

```options
{
AA_samples 3
xres 640
yres 480
GI_diffuse_depth 1
GI_diffuse_samples 3
}

plane
{
name myplane
point 0 -8 0
normal 0 1 0
}

polymesh
{
name mysph
nsides 6 1 UINT 4 4 4 4 4 4
vidxs 24 1 UINT
0 4 5 1 1 5 6 2 2 6 7 3 3 7 4 0 3 0 1 2 4 7 6 5
vlist 8 1 b64VECTOR
AAB6wwAAAAAAAHrDAAB6QwAAAAAAAHrDAAB6QwAAAAAAAHpDAAB6wwAAAAAAAHpDAAB6wwAA+kMAAHrDAAB6QwAA+kMAAHrDAAB6QwAA+kMAAHpDAAB6wwAA+kMAAHpD
smoothing on
subdiv_type catclark
subdiv_iterations 7
disp_map sphere_disp
matrix
0.94693 0 0.321439 0
0 1 0 0
-0.321439 0 0.94693 0
0 0 0 1
}

standard_surface
{
name sphere_surf
base 0.3
base_color 0.8 0.8 1
specular 1
specular_color 0.8 0.8 1
specular_roughness 0.3
subsurface 0.5
subsurface_color 1 0.05 0.2
}

nonlinear_noise
{
name sphere_disp
type perlin
freq 0.025
amplitude 80
bloom 1
}

standard_surface
{
base 1
base_color 0.4 0.4 0.4
specular 0
}

persp_camera
{
name mycamera
fov 11
position 3677.0129 1039.1904 597.0592
look_at 0 250 0
up 0 1 0
}

point_light
{
name key
position -6000 10000 6000
color 1 0.7 0.2
intensity 1
exposure 28
}

skydome_light
{
name mysky
color 0.7 0.8 0.9
intensity 0.9
}```
` `

Some examples of looks that can be obtained with this shader, along with the shader settings from the .ass file:

Lumpy Nodules

``` type abs_perlin
freq 0.025
amplitude 80```

Pomegranate

``` type recursive
freq 0.025
amplitude 40
bloom 3```

Cauliflower

``` type abs_recursive
freq 0.025
amplitude 40
bloom 3```

Brain Coral

``` type abs_perlin
freq 0.025
amplitude -40
bloom -4```
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