Somayajulu Lanka: 2007

In the previous post I have shown a picture of myself rendered using pencil and paper model. The exact paper can be found in this link.
http://pages.cpsc.ucalgary.ca/~mario/home/PhD/index.htm

I will be posting a overview of the paper and how I created the image. The pencil model as suggested in the paper includes a simulation of pencil and paper interaction. With the pencil having the properties as hardness, pencil tip shape, pressure coefficients at various points on the tip, pressure applied to the pencil, The graphite, clay and wax percentage of the pencil lead.

Each property has the following characteristics.
1. Hardness: The hardness will determine the damage done to the paper. It aalso determines how much lead is deposited on the paper. Harder the pencil less lead deposited on the paper. No description of the function used is mentioned in the paper, and we are free to use any function. But the function should have the required properties. i.e., harder the pencil more damage done and less lead deposited.

2. Pencil tip shape: This is very important because, when we draw a picture using a pencil, not only the pencil covers the pixels we have drawn but also the pixels around it. This is because the pencil shape not a infitisimal point, but a 3d volume whose volume points trace the paper depending on the pressure we have applied on the pencil. But in the simulation we just take this as a 2d polygon with pressure coefficients at the corners of the polygon ( < 1) and the polygon center, which can be decided by the programmer(or the user, or can be the exact polygon center, though this is not the case with exact pencil), has a pressure coefficient as 1. Higher the pressure coefficient more lead deposited along a particular point of the pencil.

3. Pencil pressure: Higher the pressure more lead deposited on the paper. Note this is not the pressure coefficients defined above. Once a pencil touches paper, the polygon center has a pressure equal to the pencil pressure. Other points on the pencil tip have a pressure values equal to the pressure coefficient multiplied by the pencil pressure. This final pressure value actual determines the final amount of lead or other particals deposited on the pencil.

4. The graphite lead and wax percentages of the pencil: It is studied that more the lead percentage more darker the picture will be. Similarly more the graphite percentage more harder the pencil is. And finally wax is just a lubricant for smooth traversal on the paper.
Standard pencil's graphite wax and lead percentages are given in the paper.

Paper model:
And finally the paper model is taken as a set of volumetric elements. i.e., each pixel is kind of an unstructured tank which can take in a maximum amount of pencil material.
The simulation of paper is done as a set of pixels with each pixel having different heights at its corners. So the total porus volume (ie which can take the pencil material) of the pixel is 1/4 * (sigma(heighest height - normal height)). Not the same height is being shared by all the neighbors along that particular corner. Also flatter the paper less pencil material it can take. In other words if we draw a picture on a smooth paper the drawing will be much lighter than what we get on a rough paper.

Pencil paper interaction:
Finally this is a set of mathematical elements which is best viewed in the paper. It includes how much lead material is absorbed by the paper, which depends mostly on the pressure applied on the pencil and the paper porus volume. Other elements involve snanning the pencil tip along the paper when we trace the pencil along the paper. Try to find all the pixels the pencil makes contact with and find out what the pressurer coefficient of the pencil tip is along the pixel center. This is best done bu dividing the pencil as a set of triangles and find out all the pixels traced by the triangle, and use a technique like bilinear interpolation.

Finally How I have drawn the image. First thing I have done is increasing the contrast and brightness of my picture in the photoshop, and then using pencil paper interaction at all the points of the image, with pressure applied at different points is equal to the darkness of that particular point. If you have any other questions please feel free to contact me at lankasomaya@yahoo.co.in. I think you found this information useful :)