Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!watmath!clyde!rutgers!sri-spam!mordor!lll-lcc!ames!oliveb!sun!peregrine!falk
From: falk@peregrine.UUCP
Newsgroups: comp.graphics
Subject: Re: Ray Tracing & filter references
Message-ID: <12680@sun.uucp>
Date: Wed, 4-Feb-87 01:27:57 EST
Article-I.D.: sun.12680
Posted: Wed Feb  4 01:27:57 1987
Date-Received: Thu, 5-Feb-87 05:26:09 EST
References: <179@ndmath.UUCP> <628@elrond.UUCP>
Sender: news@sun.uucp
Reply-To: falk@sun.UUCP (Ed Falk)
Organization: Sun Microsystems, Mountain View
Lines: 77
Keywords: references, ray tracing, box filters

>						...	Also,
>getting a shading algorithm isn't real easy (at least I haven't found it
>to be) because they tend to be published with lots of greek letters that
>you (and I) don't seem to like...


Ok, here's a shading algorithm in plain english.  I implemented 2/3 of
this in microcode once, so it's pretty simple.

Disclaimer: It's only a model (shh!)

There are three kinds of light that can hit and bounce off an object:
ambient, incident and specular.  Ambient light is the light that's all
around the object and illuminates it evenly from all directions.
Incident light is light that hits the surface from a particular direction;
light that hits directly (at a right angle) lights the object the most,
light that grazes the surface lights the object the least.  The angle
you *view* the surface from does not affect the brightness.  Specular
reflection is the "shininess" of the object.  Light bounces off the
surface and reaches your eye.  If you and the light source are close to
the same angle from the surface, the specular reflection is bright.

	eye	     light
           \        /
            \      /
             \    /
              \  /
        _______\/_______ surface


For example, paper has a low amount of specular reflection.  A polished
table has a high amount.

For color images, the ambient and incident reflections are the color of
the object; the specular reflection is the color of the light source.


so:

The object has three parameter that describe its appearance:  A coefficient
of incident reflection; Ci, a coefficient of specular reflection; Cs and an
exponent of specular reflection; Es.

Let A = the amount of ambient light.
I is the intensity of the light.
Let L be the vector from the surface to the light source.
E is the vector from the surface to the eye.
N is the normal vector for the surface.
R is the vector of light bouncing off the surface as if it were a mirror.
All vectors should be normalized.

R is calculated as R = 2N(N.L)-L 	["." is dot-product]
The amount of light received from ambient light is A*Ci
The amount of light received from incident light is I*Ci*(N.L)
The amount of light received from specular reflection is
I*Cs*(R.L)**Es

	Brightness = A*Ci + I*Ci*(N.L) + I*Cs*(R.L)**Es

If you have more than one light source, just sum over all of them.

Notes: Ci, Cs are values from 0 to 1.  Higher values make a brighter object.
Higher values of Cs make a shinier object.  Es varies from 8 to about 50.
Powers of two make easier computations.  Higher values make a "better
polished" impression.  Metal should have high values, things like billiard
balls should have medium values.  Experiment.

Color is not much harder.  In this case, Ci and I are (R,G,B) triples
(colored object, colored light).  Cs is still a scalar.
The red component would be

	Red = A*Ci(r) + I(r)*Ci(r)*(N.L) + I(r)*Cs*(R.L)**Es

and so forth.
		-ed falk, sun microsystems
		 sun!falk, falk@sun.com
terrorist, cryptography, DES, drugs, cipher, secret, decode, NSA, CIA, NRO.