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Add MALeaf - this combines MALeaf with MAleafViens
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and supporting functions in MAEquations.h
as well as MARotateZ to add variation
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@sambler
sambler committed Jan 25, 2013
1 parent b5c274c commit 74f2b16
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211 changes: 211 additions & 0 deletions nature/MALeaf/MAEquations.h
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/*
* MAEquations.h by Michel J. Anders (c)2013
* from https://github.com/sambler/osl-shaders
*
* license: cc-by-sa
*
* original script from -
* http://blenderthings.blogspot.nl/p/a-small-osl-libray.html
*
*/

// cubic roots adapted for OSL from http://van-der-waals.pc.uni-koeln.de/quartic/quartic.html
// so now we have a translation from Fortran -> C -> OSL. It doesn't look that well, but it works :-)

float CBRT(float Z) { return abs(pow(abs(Z),1.0/3.0)) * sign(Z); }

/*-------------------- Global Function Description Block ----------------------
*
* ***CUBIC************************************************08.11.1986
* Solution of a cubic equation
* Equations of lesser degree are solved by the appropriate formulas.
* The solutions are arranged in ascending order.
* NO WARRANTY, ALWAYS TEST THIS SUBROUTINE AFTER DOWNLOADING
* ******************************************************************
* A(0:3) (i) vector containing the polynomial coefficients
* X(1:L) (o) results
* L (o) number of valid solutions (beginning with X(1))
* ==================================================================
* 17-Oct-2004 / Raoul Rausch
* Conversion from Fortran to C
* 09-Jan-2012 / Michel Anders (varkenvarken)
* Conversion from C to OSL
*
*-----------------------------------------------------------------------------
*/

int cubic(float A[4], float X[3], int L)
{
float PI = 3.1415926535897932;
float THIRD = 1./3.;
float U[3],W, P, Q, DIS, PHI;
int i;

// ====determine the degree of the polynomial ====

if (A[3] != 0.0)
{
//cubic problem
W = A[2]/A[3]*THIRD;
P = pow((A[1]/A[3]*THIRD - pow(W,2)),3);
Q = -.5*(2.0*pow(W,3)-(A[1]*W-A[0])/A[3] );
DIS = pow(Q,2)+P;
if ( DIS < 0.0 )
{
//three real solutions!
//Confine the argument of ACOS to the interval [-1;1]!
PHI = acos(min(1.0,max(-1.0,Q/sqrt(-P))));
P=2.0*pow((-P),(5.e-1*THIRD));
for (i=0;i<3;i++)
U[i] = P*cos((PHI+2*((float)i)*PI)*THIRD)-W;
X[0] = min(U[0], min(U[1], U[2]));
X[1] = max(min(U[0], U[1]),max( min(U[0], U[2]), min(U[1], U[2])));
X[2] = max(U[0], max(U[1], U[2]));
L = 3;
}
else
{
// only one real solution!
DIS = sqrt(DIS);
X[0] = CBRT(Q+DIS)+CBRT(Q-DIS)-W;
L=1;
}
}
else if (A[2] != 0.0)
{
// quadratic problem
P = 0.5*A[1]/A[2];
DIS = pow(P,2)-A[0]/A[2];
if (DIS > 0.0)
{
// 2 real solutions
X[0] = -P - sqrt(DIS);
X[1] = -P + sqrt(DIS);
L=2;
}
else
{
// no real solution
L=0;
}
}
else if (A[1] != 0.0)
{
//linear equation
X[0] =A[0]/A[1];
L=1;
}
else
{
//no equation
L=0;
}
/*
* ==== perform one step of a newton iteration in order to minimize
* round-off errors ====
*/
for (i=0;i < L;i++)
{
X[i] = X[i] - (A[0]+X[i]*(A[1]+X[i]*(A[2]+X[i]*A[3])))
/(A[1]+X[i]*(2.0*A[2]+X[i]*3.0*A[3]));
}

return 0;
}


point cubicspline(float t, point P0, point P1, point P2, point P3)
{
return (1-t)*(1-t)*(1-t)*P0
+ 3*(1-t)*(1-t)*t*P1
+ 3*(1-t)*t*t*P2
+ t*t*t*P3;

// how to group all factors of the powers of t
//
// (1-2t+t2-t+2t2+t3)P0 => (1-3t+3t2+t3)P0
// (3t-6t2+3t3)P1
// (3t2-3t3)P2
// t3P3
//
// 1 * ( P0 )
// t * ( 3P0+3P1 )
// t2* ( 3P0-6P1+3P2 )
// t3* ( P0+3P1-3P2+P3)
}

// calculate the closest distance from Pos to a quadratic bezier curve
// the curve is defined by the 3 points P0, P1 and P2

int splinedist(point p0, point p1, point p2, point Pos, float d, float tc)
{

point P0 = p0;
point P1 = p1;
point P2 = p2;

// following definitions are for the four polynomic coefficients for the well known
// equation dB/dt . (Pos-B) (i.e. the inproduct of the tangent to the bezier and the
// difference vector from the point under considertion to the Bezier curve.
// If the difference vector is perpendicular to the tangent we have found a closest point
// on the Bezier curve.
// The stuff below is generated by a script and no effort is spent on collecting factors.
// We let the OSL compiler worry about that :-)

float t0 = -2*P0[0]*P0[0]+-2*P1[0]*Pos[0]+2*P0[0]*P1[0]+2*P0[0]*Pos[0]
+-2*P0[1]*P0[1]+-2*P1[1]*Pos[1]+2*P0[1]*P1[1]+2*P0[1]*Pos[1]
+-2*P0[2]*P0[2]+-2*P1[2]*Pos[2]+2*P0[2]*P1[2]+2*P0[2]*Pos[2];

float t1 = -4*P0[0]*P1[0]+-4*P0[0]*P1[0]+-4*P0[0]*P1[0]+-2*P0[0]*Pos[0]
+-2*P2[0]*Pos[0]+2*P0[0]*P0[0]+2*P0[0]*P2[0]+4*P0[0]*P0[0]
+4*P1[0]*P1[0]+4*P1[0]*Pos[0]+-4*P0[1]*P1[1]+-4*P0[1]*P1[1]
+-4*P0[1]*P1[1]+-2*P0[1]*Pos[1]+-2*P2[1]*Pos[1]+2*P0[1]*P0[1]
+2*P0[1]*P2[1]+4*P0[1]*P0[1]+4*P1[1]*P1[1]+4*P1[1]*Pos[1]
+-4*P0[2]*P1[2]+-4*P0[2]*P1[2]+-4*P0[2]*P1[2]+-2*P0[2]*Pos[2]
+-2*P2[2]*Pos[2]+2*P0[2]*P0[2]+2*P0[2]*P2[2]+4*P0[2]*P0[2]
+4*P1[2]*P1[2]+4*P1[2]*Pos[2];

float t2 = -8*P1[0]*P1[0]+-4*P0[0]*P0[0]+-4*P0[0]*P2[0]+-4*P1[0]*P1[0]
+-2*P0[0]*P0[0]+-2*P0[0]*P2[0]+2*P0[0]*P1[0]+2*P1[0]*P2[0]
+4*P0[0]*P1[0]+4*P0[0]*P1[0]+4*P1[0]*P2[0]+8*P0[0]*P1[0]
+-8*P1[1]*P1[1]+-4*P0[1]*P0[1]+-4*P0[1]*P2[1]+-4*P1[1]*P1[1]
+-2*P0[1]*P0[1]+-2*P0[1]*P2[1]+2*P0[1]*P1[1]+2*P1[1]*P2[1]
+4*P0[1]*P1[1]+4*P0[1]*P1[1]+4*P1[1]*P2[1]+8*P0[1]*P1[1]
+-8*P1[2]*P1[2]+-4*P0[2]*P0[2]+-4*P0[2]*P2[2]+-4*P1[2]*P1[2]
+-2*P0[2]*P0[2]+-2*P0[2]*P2[2]+2*P0[2]*P1[2]+2*P1[2]*P2[2]
+4*P0[2]*P1[2]+4*P0[2]*P1[2]+4*P1[2]*P2[2]+8*P0[2]*P1[2];

float t3 = -4*P0[0]*P1[0]+-4*P0[0]*P1[0]+-4*P1[0]*P2[0]+-4*P1[0]*P2[0]
+2*P0[0]*P0[0]+2*P0[0]*P2[0]+2*P0[0]*P2[0]+2*P2[0]*P2[0]
+8*P1[0]*P1[0]+-4*P0[1]*P1[1]+-4*P0[1]*P1[1]+-4*P1[1]*P2[1]
+-4*P1[1]*P2[1]+2*P0[1]*P0[1]+2*P0[1]*P2[1]+2*P0[1]*P2[1]
+2*P2[1]*P2[1]+8*P1[1]*P1[1]+-4*P0[2]*P1[2]+-4*P0[2]*P1[2]
+-4*P1[2]*P2[2]+-4*P1[2]*P2[2]+2*P0[2]*P0[2]+2*P0[2]*P2[2]
+2*P0[2]*P2[2]+2*P2[2]*P2[2]+8*P1[2]*P1[2];

float A[4] = {t0,t1,t2,t3};
float T[3] ;
int n ;
cubic(A,T,n);
d = 1e6;
// cubic() will return 0 , 1 or 3 values for t
// we are only interested in values that lie in the interval [0,1]
// for those we calculate the position on the curve and check whether
// we have found the shortest distance.
int found = 0;
while(n>0){
n--;
if(T[n]>=0 && T[n]<=1){
float t = T[n];
found = 1;
float dd = distance((1-t)*(1-t)*P0 + 2*(1-t)*t *P1 + t*t*P2, Pos);
if (dd < d) {
d = dd;
tc = t;
}
}
}
return found;
}


86 changes: 86 additions & 0 deletions nature/MALeaf/MALeaf.osl
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/*
* MALeaf.osl by Michel J. Anders (c)2013
* from https://github.com/sambler/osl-shaders
*
* license: cc-by-sa
*
* original script from -
* http://blenderthings.blogspot.com.au/2013/01/a-osl-leaf-shape-shader-for-cycles.html
*
*/

#include "stdosl.h"
#include "MAEquations.h"

shader leaf(
point Vector = P,
float BaseAngle = 107.0,
float BaseCurve = 0.7,
float TipAngle = 44.0,
float TipCurve = 1.2,
output float Leaf = 0 )
{
// calculate the four control point of the cubic spline
float x1,y1,x2,y2;
sincos(radians(BaseAngle),y1,x1);
sincos(radians(TipAngle),y2,x2);
point P0 = point(0, 0, 0);
point P1 = point(x1, y1, 0)*BaseCurve;
point P2 = point(1-x2*TipCurve, y2*TipCurve, 0);
point P3 = point(1, 0, 0);

// to determin the y value(s) of the spline at the x position we
// are located, we want to solve spline(t) - x = 0
// we therefore gather all factors and solve the cubic equation
float tfactor[4] = { P0[0]-Vector[0],
3*P0[0]+3*P1[0],
3*P0[0]-6*P1[0]+3*P2[0],
P0[0]+3*P1[0]-3*P2[0]+P3[0] };
float t[3];
int nrealroots;
cubic(tfactor, t, nrealroots);

// at this point, the array t holds up to 3 real roots
// remove any real root that is not in range [0,1]
int i=0;
while(i < nrealroots){
if ((t[i] < 0) || (t[i] > 1)) {
int j=i;
while(j < (nrealroots-1)){
t[j]=t[j+1];
j++;
}
nrealroots--;
}
i++;
}

// note that a cubic funtion can have 3 real roots,
// but in this case we ignore such very warped curves
// TODO: w. 3 real roots w could set leaf = 1, if y < y0 OR y between y1,y2
// TODO: seration, possible by determining the closest
// distance (if inside leaf) to the spline and
// determining if w are within some periodic funtion f(t)

// we generate the shape mirrored about the x-axis
float y = Vector[1];
if(y<0) y = -y;

if(nrealroots > 0){
point Sy0 = cubicspline(t[0],P0,P1,P2,P3);
if(nrealroots > 1){
// if we have 2 roots we calculate and order the y values
// and check whether the current y values is between them
point Sy1 = cubicspline(t[1],P0,P1,P2,P3);
if ( Sy1[1] < Sy0[1] ){
if( (y > Sy1[1]) && (y < Sy0[1]) ) Leaf = 1;
}else{
if( (y > Sy0[1]) && (y < Sy1[1]) ) Leaf = 1;
}
}else{
// with a single value we check if we are below the y value
if( y < Sy0[1] ) Leaf = 1;
}
}
}

92 changes: 92 additions & 0 deletions nature/MALeaf/MALeafVeins.osl
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/*
* MALeafVeins.osl by Michel J. Anders (c)2013
* from https://github.com/sambler/osl-shaders
*
* license: cc-by-sa
*
* original script from -
* http://blenderthings.blogspot.com.au/2013/01/osl-leaf-veins-shader-for-cycles.html
*
*/

#include "stdosl.h"
#include "MAEquations.h"

shader arcuateveins(
point Vector = P,

float BaseAngle = 107.0,
float BaseCurve = 0.7,
float TipAngle = 44.0,
float TipCurve = 1.2,

int Veins = 7,
int Seed = 42,
float Variance = 0,
float InnerWidth = 0.05,
float NWidth = 0.25, // size of the reticulated area

float Curve = 0.5, // distribution of endpoints on edge
float Curve2 = 0.5, // distribution of controlpoints
float Spacing = 0.5, // distribution of starting points
float Up = 0.5,

output float Vein = 0,
output float Net = 0,
output float Fac = 0 )
{

float delta = 1.0/((float)Veins+1);
float delta2= delta/2;
float delta4= delta/4;

// calculate the four control points of the cubic spline that defines the leaf edge
float x1,y1,x2,y2;
sincos(radians(BaseAngle),y1,x1);
sincos(radians(TipAngle),y2,x2);
point P0 = point(0, 0, 0);
point P1 = point(x1, y1, 0)*BaseCurve;
point P2 = point(1-x2*TipCurve, y2*TipCurve, 0);
point P3 = point(1, 0, 0);

point P0q = point(P0[0],P0[1]*Up,P0[2]);
point P1q = point(P1[0],P1[1]*Up,P1[2]);
point P2q = point(P2[0],P2[1]*Up,P2[2]);
point P3q = point(P3[0],P3[1]*Up,P3[2]);

int i;
for(i=0;i < Veins;i++){

// determine the starting points of the veins
float x = (i*delta+delta2*Variance*cellnoise(i+10+Seed))*Spacing;
float dx = (delta4*Variance*cellnoise(i+17+Seed))*Spacing;
point P0up = point(delta2+x+dx,0,0);
point P0down = point(delta2+x,0,0);
// determine the endpoints on the leaf edge
float t=(i*delta+delta2)*Curve+1-Curve;
point P2up = cubicspline(t,P0,P1,P2,P3);
point P2down = point(P2up[0],-P2up[1],P2up[2]);
// the veins are quadratic splines, so need one additional control point
t=(i*delta+delta2)*Curve2+1-Curve2;
point P1up = cubicspline(t,P0q,P1q,P2q,P3q);
point P1down = point(P1up[0],-P1up[1],P1up[2]);

float r;
int f = splinedist(P0up, P1up, P2up, Vector, r, t);
if ( f && (r < NWidth ) ) Net = 1 ;
if ( f && (r < InnerWidth * ( 1- t) * (1-Vector[0]) ) ) {
Vein = 1; Fac = sqrt(1-r/InnerWidth); break;
}
f = splinedist(P0down, P1down, P2down, Vector, r , t);
if ( f && (r < NWidth ) ) Net = 1 ;
if ( f && (r < InnerWidth * ( 1- t) * (1-Vector[0]) ) ) {
Vein = 1; Fac = sqrt(1-r/InnerWidth); break;
}
}

// the central vein
float d = distance(point(0,0,0),point(1,0,0),Vector);
if ( d < NWidth ) Net = 1 ;
if (d < (InnerWidth * (1-Vector[0])) ) { Vein = 1; Fac = sqrt(1-d/InnerWidth);}
}

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