# Neural Network SDFs

calendar_today

01.01.2024

label

Python

mouse

Houdini 20

### Description

Shadertoy artist Blackle Mori modified a neural network to convert meshes to signed distances stored as matrices. How to use this neural network is explained in the video below.

### 1 Code

The relatively compact code below multiplies matrices and sine waves in order to shape the famous Stanford Bunny, effectively making it resolution-independent.

``````// (c) by blackle mori

function float scene(vector p){
if(length(p) > 1.0) {
return length(p) - 0.8;
}

vector4 f00 = sin(p.z * set(-3.02,1.95,-3.42,-.60)   + p.y * set(3.08,.85,-2.25,-.24)   - p.x * set(-.29,1.16,-3.74,2.89) + set(-.71,4.50,-3.24,-3.50));
vector4 f01 = sin(p.z * set(-.40,-3.61,3.23,-.14)    + p.y * set(-.36,3.64,-3.91,2.66)  - p.x * set(2.90,-.54,-2.75,2.71) + set(7.02,-5.41,-1.12,-7.41));
vector4 f02 = sin(p.z * set(-1.77,-1.28,-4.29,-3.20) + p.y * set(-3.49,-2.81,-.64,2.79) - p.x * set(3.15,2.14,-3.85,1.83) + set(-2.07,4.49,5.33,-2.17));
vector4 f03 = sin(p.z * set(-.49,.68,3.05,.42)       + p.y * set(-2.87,.78,3.78,-3.41)  - p.x * set(-2.65,.33,.07,-.64)   + set(-3.24,-5.90,1.14,-4.71));

vector4 f10 = sin(set(-.34,.06,-.59,-.76,.10,-.19,-.12,.44,.64,-.02,-.26,.15,-.16,.21,.91,.15)      * f00 +
set(.01,.54,-.77,.11,.06,-.14,.43,.51,-.18,.08,.39,.20,.33,-.49,-.10,.19)         * f01 +
set(.27,.22,.43,.53,.18,-.17,.23,-.64,-.14,.02,-.10,.16,-.13,-.06,-.04,-.36)      * f02 +
set(-.13,.29,-.29,.08,1.13,.02,-.83,.32,-.32,.04,-.31,-.16,.14,-.03,-.20,.39)     * f03 +
set(.73,-4.28,-1.56,-1.80))/1.0                                                   + f00;

vector4 f11 = sin(set(-1.11,.55,-.12,-1.00,.16,.15,-.30,.31,-.01,.01,.31,-.42,-.29,.38,-.04,.71)    * f00 +
set(.96,-.02,.86,.52,-.14,.60,.44,.43,.02,-.15,-.49,-.05,-.06,-.25,-.03,-.22)     * f01 +
set(.52,.44,-.05,-.11,-.56,-.10,-.61,-.40,-.04,.55,.32,-.07,-.02,.28,.26,-.49)    * f02 +
set(.02,-.32,.06,-.17,-.59,.00,-.24,.60,-.06,.13,-.21,-.27,-.12,-.14,.58,-.55)    * f03 +
set(-2.24,-3.48,-.80,1.41))/1.0                                                   + f01;

vector4 f12 = sin(set(.44,-.06,-.79,-.46,.05,-.60,.30,.36,.35,.12,.02,.12,.40,-.26,.63,-.21)        * f00 +
set(-.48,.43,-.73,-.40,.11,-.01,.71,.05,-.25,.25,-.28,-.20,.32,-.02,-.84,.16)     * f01 +
set(.39,-.07,.90,.36,-.38,-.27,-1.86,-.39,.48,-.20,-.05,.10,-.00,-.21,.29,.63)    * f02 +
set(.46,-.32,.06,.09,.72,-.47,.81,.78,.90,.02,-.21,.08,-.16,.22,.32,-.13)         * f03 +
set(3.38,1.20,.84,1.41))/1.0                                                      + f02;

vector4 f13 = sin(set(-.41,-.24,-.71,-.25,-.24,-.75,-.09,.02,-.27,-.42,.02,.03,-.01,.51,-.12,-1.24) * f00 +
set(.64,.31,-1.36,.61,-.34,.11,.14,.79,.22,-.16,-.29,-.70,.02,-.37,.49,.39)       * f01 +
set(.79,.47,.54,-.47,-1.13,-.35,-1.03,-.22,-.67,-.26,.10,.21,-.07,-.73,-.11,.72)  * f02 +
set(.43,-.23,.13,.09,1.38,-.63,1.57,-.20,.39,-.14,.42,.13,-.57,-.08,-.21,.21)     * f03 +
set(-.34,-3.28,.43,-.52))/1.0                                                     + f03;

f00 = sin(set(-.72,.23,-.89,.52,.38,.19,-.16,-.88,.26,-.37,.09,.63,.29,-.72,.30,-.95)               * f10 +
set(-.22,-.51,-.42,-.73,-.32,.00,-1.03,1.17,-.20,-.03,-.13,-.16,-.41,.09,.36,-.84)        * f11 +
set(-.21,.01,.33,.47,.05,.20,-.44,-1.04,.13,.12,-.13,.31,.01,-.34,.41,-.34)               * f12 +
set(-.13,-.06,-.39,-.22,.48,.25,.24,-.97,-.34,.14,.42,-.00,-.44,.05,.09,-.95)             * f13 +
set(.48,.87,-.87,-2.06))/1.4                                                              + f10;

f01 = sin(set(-.27,.29,-.21,.15,.34,-.23,.85,-.09,-1.15,-.24,-.05,-.25,-.12,-.73,-.17,-.37)         * f10 +
set(-1.11,.35,-.93,-.06,-.79,-.03,-.46,-.37,.60,-.37,-.14,.45,-.03,-.21,.02,.59)          * f11 +
set(-.92,-.17,-.58,-.18,.58,.60,.83,-1.04,-.80,-.16,.23,-.11,.08,.16,.76,.61)             * f12 +
set(.29,.45,.30,.39,-.91,.66,-.35,-.35,.21,.16,-.54,-.63,1.10,-.38,.20,.15)               * f13 +
set(-1.72,-.14,1.92,2.08))/1.4                                                            + f11;

f02 = sin(set(1.00,.66,1.30,-.51,.88,.25,-.67,.03,-.68,-.08,-.12,-.14,.46,1.15,.38,-.10)            * f10 +
set(.51,-.57,.41,-.09,.68,-.50,-.04,-1.01,.20,.44,-.60,.46,-.09,-.37,-1.30,.04)           * f11 +
set(.14,.29,-.45,-.06,-.65,.33,-.37,-.95,.71,-.07,1.00,-.60,-1.68,-.20,-.00,-.70)         * f12 +
set(-.31,.69,.56,.13,.95,.36,.56,.59,-.63,.52,-.30,.17,1.23,.72,.95,.75)                  * f13 +
set(-.90,-3.26,-.44,-3.11))/1.4                                                           + f12;

f03 = sin(set(.51,-.98,-.28,.16,-.22,-.17,-1.03,.22,.70,-.15,.12,.43,.78,.67,-.85,-.25)             * f10 +
set(.81,.60,-.89,.61,-1.03,-.33,.60,-.11,-.06,.01,-.02,-.44,.73,.69,1.02,.62)             * f11 +
set(-.10,.52,.80,-.65,.40,-.75,.47,1.56,.03,.05,.08,.31,-.03,.22,-1.63,.07)               * f12 +
set(-.18,-.07,-1.22,.48,-.01,.56,.07,.15,.24,.25,-.09,-.54,.23,-.08,.20,.36)              * f13 +
set(-1.11,-4.28,1.02,-.23))/1.4                                                           + f13;

return dot(f00, set(.09,.12,-.07,-.03)) + dot(f01, set(-.04,.07,-.08,.05)) +
dot(f02, set(-.01,.06,-.02,.07)) + dot(f03, set(-.05,.07,.03,.04)) - 0.16;

}

f@d = scene(v@P);``````