From 74f2b16668316bf7c9a44485e6e5fa791bae4c84 Mon Sep 17 00:00:00 2001 From: sambler Date: Fri, 25 Jan 2013 22:40:53 +1030 Subject: [PATCH] Add MALeaf - this combines MALeaf with MAleafViens and supporting functions in MAEquations.h as well as MARotateZ to add variation --- nature/MALeaf/MAEquations.h | 211 +++++++++++++++++++++++ nature/MALeaf/MALeaf.osl | 86 +++++++++ nature/MALeaf/MALeafVeins.osl | 92 ++++++++++ nature/MALeaf/MALeafWithVeins.bcm | 84 +++++++++ nature/MALeaf/MALeafWithVeins.jpg | Bin 0 -> 10825 bytes nature/MALeaf/MALeafWithVeins.noodle.jpg | Bin 0 -> 190497 bytes nature/MALeaf/MARotateZ.osl | 21 +++ 7 files changed, 494 insertions(+) create mode 100644 nature/MALeaf/MAEquations.h create mode 100644 nature/MALeaf/MALeaf.osl create mode 100644 nature/MALeaf/MALeafVeins.osl create mode 100644 nature/MALeaf/MALeafWithVeins.bcm create mode 100644 nature/MALeaf/MALeafWithVeins.jpg create mode 100644 nature/MALeaf/MALeafWithVeins.noodle.jpg create mode 100644 nature/MALeaf/MARotateZ.osl diff --git a/nature/MALeaf/MAEquations.h b/nature/MALeaf/MAEquations.h new file mode 100644 index 0000000..61c3578 --- /dev/null +++ b/nature/MALeaf/MAEquations.h @@ -0,0 +1,211 @@ +/* + * 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; +} + + diff --git a/nature/MALeaf/MALeaf.osl b/nature/MALeaf/MALeaf.osl new file mode 100644 index 0000000..08bc247 --- /dev/null +++ b/nature/MALeaf/MALeaf.osl @@ -0,0 +1,86 @@ +/* + * 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; + } + } +} + diff --git a/nature/MALeaf/MALeafVeins.osl b/nature/MALeaf/MALeafVeins.osl new file mode 100644 index 0000000..07cbdcc --- /dev/null +++ b/nature/MALeaf/MALeafVeins.osl @@ -0,0 +1,92 @@ +/* + * 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);} +} + diff --git a/nature/MALeaf/MALeafWithVeins.bcm b/nature/MALeaf/MALeafWithVeins.bcm new file mode 100644 index 0000000..54c7ac2 --- /dev/null +++ b/nature/MALeaf/MALeafWithVeins.bcm @@ -0,0 +1,84 @@ + + + + + + + + + + + + + + + + + + + + + + + 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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" + +shader rotate_z( + point Vector = P, + float Angle = 0, + output point VecOut = P ) +{ + VecOut = rotate(Vector,radians(Angle),point(0,0,0),point(0,0,1)); +} +