OSL leaf veins shader for Cycles

When we look at images the addition of veins greatly adds to the preceived realism of rendered leaves and in this article I present a simple veins shader that complements the leaf shader discussed previously.

Leaf veins

I forgot to update the page that describes equations.h (thanks samblerdevel for pointing that out). I just corrected that so if you had any errors complaining abot a function splinedist() that was missing, download & install equations.h and try again

The node setup used to create the leaf shape and veination in the close-up image above is relatievely complicated and presented at the end of this article. Luckily, the basic stuff of generating vein patterns is not that complicated so lets have a look at that first.

As illustrated in the images above the veins in the leaf are all represented by cubic splines, starting at the red dots on the central vein and curving to the green end points on the edge of the leaf. Their curvature is controled by the blue control points. A node setup for the image above looks like this:

The Angle and L parameters mimic the ones in the leaf shape shader and are kept the same in this case to let the endpoints of the veins coincide with the actual leaf edge. The number of veins, their distribution, width and the way they curve are controlled by the Veins, Width, Squish and Up parameters as we will see later on. Their is some randomness in the placement as well which can bee influenced by the Seed and Var parameters. The outputs consist chiefly of a Vein socket which will be one for a vein, and a Fac socket which is the square root of the distance to the center of the vein and can be used to drive displacement.

The code for this node is shown below makes use of the equations.h include discussed in the article on leaf shapes.

#include "equations.h"

shader arcuateveins(
 point Pos = P,
 int Veins = 7,
 int Seed = 42,
 float Var = 0,
 float Width = 0.05,
 float NWidth = 0.25, // size of the reticulated area
 
 float Squish  = 0.5, // distribution of endpoints on edge
 float Squish2 = 0.5, // distribution of controlpoints
 float Squish3 = 0.5, // distribution of starting points
 float Up = 0.5,
 
 float Angle1 = 70,
 float L1 = 1,
 float Angle2 = 70,
 float L2 = 1,
 
 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(Angle1),y1,x1);
 sincos(radians(Angle2),y2,x2);
 point P0 = point(0      , 0 ,0);
 point P1 = point(x1     , y1,0)*L1;
 point P2 = point(1-x2*L2, y2*L2,0);
 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*Var*cellnoise(i+10+Seed))*Squish3;
  float dx = (delta4*Var*cellnoise(i+17+Seed))*Squish3;
  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)*Squish+1-Squish;
  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)*Squish2+1-Squish2;
  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, Pos, r, t);
  if ( f && (r < NWidth ) ) Net = 1 ;
  if ( f && (r < Width * ( 1- t) * (1-Pos[0]) ) ) { Vein = 1; Fac = sqrt(1-r/Width); break; }
  f = splinedist(P0down, P1down, P2down, Pos, r , t);
  if ( f && (r < NWidth ) ) Net = 1 ;
  if ( f && (r < Width * ( 1- t) * (1-Pos[0]) ) ) { Vein = 1; Fac = sqrt(1-r/Width); break; }
 }
 
 // the central vein
 float d = distance(point(0,0,0),point(1,0,0),Pos);
 if ( d < NWidth ) Net = 1 ;
 if (d < (Width * (1-Pos[0])) ) { Vein = 1; Fac = sqrt(1-d/Width);}
}

Relation to real venation patterns in leaves

The shader in its current form is able to model pinnate and arcuate venation patters and intermediate forms of these. (For an explanation of terminolgy refer to Wikipedia, especially this overview sheet). Its spline-based modelling of the veins is not based on any underlying theory of the formation of veins as it happens in nature, as these reaction-diffusion equations cannot so easily be implemented in an OSL shader (at least not at present: we wouldn't want to redo such a costly simulation again and again for each point being shaded so we would need peform the simulation before we start shading each pixel. Currently there is no facility for adding something to a shader that will be executed once beforehand, although there might be in the future. An alternative approach might be to perform the simulation, maybe in a Python add-on, and store the result in a texture. Here we opted for art before science: if it looks all right we don't care what it is based on).

Controlling the curve shape of the veins

In the following images I have illustrated how you can control the shape of the veins. How much the starting points on the central vein and the control points in the middle and the end points on the leaf edge are bunched up, is controlled by the Squish parameters. The blue control points all lie on a spline that is a copy of the spline that defines the leaf edge by scaled by the Up parameter. Some experimenting shows that is is possible to create both pinnate venation patterns as well as arcuate patterns:

Example node setup

The leaves in the image at the top of this article were created with the following node setup:

The values in the blue box simultaneously control the shape of the leaf edge both in the leaf shader and in the vein shader. The leaf coloring is controled by the nodes in the green box (leaves are both glossy and translucent) while the vein coloring is is defined by the nodes in the red box, the choice being determined by the Vein output socket of the vein shader. The yellow box provides some noisy patterns to drive both the colloration of the leaf as well as mix with the bump patern from the vein shader to drive the displacement. The exact contribution of these displacements is controlled by the purple nodes.

Room for improvement

Although the shader is already quite versatile there is ample room for imrpovement. For example, I would like it to be able to produce palmate vein patters and to control the narrowing towards the tips of the veins. On the other hand the shader is not limited to producing vein pattersn: I imagine it can be used to produce fish bones and bird feather patterns (barbs) as well. I might expand on that in the future.

A OSL leaf shape shader for Cycles

In this first part of a series I present a simple shader that can be used to generate different leaf shapes. In later articles we will add shaders that produce the veins of the leaf.

Simple leaf shape with cubic splines

In the example image we have used the IvyGen addon to generate a single limb of some climbing plant species and used the shader from this article to produce the leaf shapes The node setup for this specific material is dicussed later on. (the stone texture is from cgtextures.com and was converted to a normal map and a displacement map with Shadermap CL. The backplate and environment lighting are from the Topanga Forest B collection by Blochi as found on Sibl archive)

The leaf shape shader is essentially creates one side of a leaf from a cubic spline and mirrors that to the other side to create a symmetrical shape. The spline that is used has four controls.

It starts on the left in the direction of P1 and ends on the right coming from the direction of P2. The lenght and angles of the vectors going to P1 and P2 are inputs to the shader. Some of the shapes you can create are shown below.

Note that it is also possible to define a shape that crosses itself in which case the behavior of the shader is undefined.

The annotated code for the shader is shown below. It includes a small library of functions that will be reused by shaders that will appear on this blog in the near future and this include has its separate page where you can download it and find installation instructions.

#include "equations.h"

shader leaf(
 point Pos = P,
 float Angle1 = 70,
 float L1 = 1,
 float Angle2 = 70,
 float L2 = 1,
 output float Leaf = 0
){

 // calculate the four control point of the cubic spline
 float x1,y1,x2,y2;
 sincos(radians(Angle1),y1,x1);
 sincos(radians(Angle2),y2,x2);
 point P0 = point(0      , 0 ,0);
 point P1 = point(x1     , y1,0)*L1;
 point P2 = point(1-x2*L2, y2*L2,0);
 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]-Pos[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 = Pos[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;
  }
 }
}

Example node setup

The node setup used to create the sample shapes look like this:

As you can see there is nothing fancy going on here. The leaves are simple squares with a reset uv-map and a mapping node is used to position the leave onto this square (in this case rotated 90 degrees). The output of the shader is then used to drive a mix shader which shows some green material where there is a leaf and a fully transparent material where there isn't.

Combining things with the Ivy Generator

The sample image at the beginning was create with the IvyGen addon. The leaves it produces are simple square faces that are not connected but nevertheless consist of a single mesh object. Because we want to orient each individual leaf a bit different we need a random number for each leaf. We therefore have to separate each face into its own object.

The workflow to achieve that then becomes:

1. Create your ivy
2. Assign the material shown in the noodle below to the leaf object
3. Goto edit mode
4. Select all
5. Select Mesh->Vertices->Separate->By loose parts
6. Go back to object mode.

Each leaf now is its own object we our leaf material attacthed.

Example node setup II

The noodle consists of three distinct parts:

• The green part adds a small random rotation around the z axis to each uv map. This will be different for each individual leaf. The actual rotation is done by another OSL shader (given below) because the vector mapping node cannot be driven by inputs.
• The red part maps the rotated uv to the correct position before handing it to our leaf shader. This mapping is necessary because the squares created by IvyGen are sort of centered on the vines and we want our leaves to protrude from the vined instead of being pierced by them.
• The blue part is just a simple mottled green shader with some gloss.

The rotation of the uv-map arond the z-axis is performed by an OSL shader because the vector mapping node has no inputs to control the rotation and it would take a lot of vector math nodes to achieve what we want whereas thanks to OSL this rotation is a no-brainer:

shader rotate_z(
 point Pos = P,
 float Angle = 0,
 output point Pout = P
){
 Pout = rotate(Pos,radians(Angle),point(0,0,0),point(0,0,1));
}

Next steps

In a next article I will show how to add veins to the leaf shapes.