# Basic Illumination Model in C#

, 9 Apr 2013 GPL3
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Basic illumination model in C#.
 Ambient Diffuse Specular Ambient+Diffuse Diffuse+Specular Ambient+Diffuse+Specular

## Introduction

In my previous article Simple Ray Tracing in C#, we saw how to display spheres using a simple ray tracing algorithm. Now, we will start from the last point and will work with basic illumination models.

By definition, we have three types of light:

• Ambient
• Diffuse
• Specular

#### Ambient

It is considered as the light distributed by the environment, which contributes to the global illumination independent of the light position, objects, or observer.

#### Diffuse

It is the light the contribution of which depends on its incidence angle. Diffuse light hit can be reflected in all directions.

#### Specular

Specular lights represent the bright spots in objects; the more reflective it is the smaller the bright spot.

## Background

To proceed with an illumination algorithm, we need to get the ambient, diffuse, and specular constants for the material we want to model; for example, here we use brass constants which are:

 K Ambient Diffuse Specular RED 0.329412 0.780392 0.992157 GREEN 0.223529 0.568627 0.941176 BLUE 0.027451 0.113725 0.807843

Exponent 27.8974

The ray tracing algorithm used is the same as you can see on Simple Ray Tracing in C# with the improvements of a basic illumination model.

## The Equations

A Light Source is defined as an R3 (x,y,z) point with a (vx,vy,vz) direction vector.

An Observer is defined as an R3 (x,y,z) point with a (vx,vy,vz) direction vector.

Theta is defined as the angle between a light ray and a normal vector at the intersection point P on the surface.

Phi is defined as the angle between the reflected light ray at the intersection point P on the surface and the viewer ray to the same point P.

#### The Sphere Equation

• r2 = (x-cx)2+(y-cy)2+(z-cz)2

#### Illumination on a given pixel:

• IAmbient = I * KAmbient
• IDiffuse = I * KDiffuse * cos(theta)
• ISpecular = I * KSpecular * cos(phi)n
• I = IAmbient + IDiffuse + ISpecular

#### Reflection calculation:

• i' = i - (2 * n * dot(i, n))

where

• i = incidence light ray
• n = normal at intersection
• i' = reflected ray

## The Code

```...
if (spherehit != null)
{
double intersx  = px + t * vx, intersy = py + t * vy,
intersz = pz + t * vz;
double vNormalX = intersx - spherehit.cx,
vNormalY=intersy - spherehit.cy,
vNormalZ=intersz - spherehit.cz;
double cost     = tAlgebra.GetCosAngleV1V2(lvx, lvy, lvz, vNormalX,
vNormalY, vNormalZ);
if (cost < 0) cost = 0;

double vReflX = 0, vReflY = 0, vReflZ = 0;
double vEye2IntersX = px - intersx, vEye2IntersY = py - intersy,
vEye2IntersZ = pz - intersz;

tAlgebra.Reflect(lvx,lvy,lvz, vNormalX,vNormalY,vNormalZ,ref vReflX,
ref vReflY, ref vReflZ);
double cosf = tAlgebra.GetCosAngleV1V2(vReflX, vReflY, vReflZ,
vEye2IntersX, vEye2IntersY, vEye2IntersZ);
if (cosf < 0) cosf = 0;

double result1 = cost * 255.0;
double result2 = Math.Pow(cosf, spherehit.shininess) * 255.0;
double rgbR = (spherehit.ambientR * 255.0)+(spherehit.diffuseR *
result1) + (spherehit.specularR * result2);
double rgbG = (spherehit.ambientG * 255.0) +(spherehit.diffuseG *
result1) + spherehit.specularG * result2);
double rgbB = (spherehit.ambientB * 255.0) +(spherehit.diffuseB *
result1) + (spherehit.specularB * result2);
rgbR = Math.Min(rgbR, 255);
rgbG = Math.Min(rgbG, 255);
rgbB = Math.Min(rgbB, 255);
color = Color.FromArgb((int)rgbR, (int)rgbG, (int)rgbB);
...
}
...```

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 First Prev Next
 How can I do this on my project? tazugur 16-Aug-13 6:35
 Re: How can I do this on my project? andalmeida 21-Aug-13 9:14
 Re: How can I do this on my project? tazugur 21-Aug-13 9:58
 Re: How can I do this on my project? andalmeida 21-Aug-13 10:03
 Re: How can I do this on my project? tazugur 21-Aug-13 10:29
 Re: How can I do this on my project? andalmeida 21-Aug-13 10:06
 Re: How can I do this on my project? tazugur 21-Aug-13 10:16
 Re: How can I do this on my project? andalmeida 21-Aug-13 10:19
 My vote of 5 manoj kumar choubey 26-Feb-12 22:16
 Last article on Raytracing andalmeida 29-Apr-09 3:03
 Specular Highlight [modified] efi_germany 3-Aug-07 9:43
 Re: Specular Highlight andalmeida 3-Aug-07 10:01
 Hi,   the observer and light are on same side of object for those tracings...   Follows the settings:   // observer/eye/camera double px = 0.0; double py = 0.0; double pz = 600.0;   // light position double lpx = 200.0; double lpy = 200.0; double lpz = 200.0;   // sphere centered at (0,0,90) radius=100 tSphere sph1 = new tSphere(0.0, 0.0, 90.0, 100.0, 0.0, 0.0, 255.0); // ambient properties for the material sph1.ambientR = 0.329412; sph1.ambientG = 0.223529; sph1.ambientB = 0.027451;   // specular properties for the material sph1.specularR = 0.992157; sph1.specularG = 0.941176; sph1.specularB = 0.807843; sph1.shininess = 27.8974;   sph1.diffuseR = 0.780392; sph1.diffuseG = 0.568627; sph1.diffuseB = 0.113725;   double intersx = px + t * vx, intersy = py + t * vy, intersz = pz + t * vz; double vNormalX = intersx - spherehit.cx, vNormalY=intersy - spherehit.cy, vNormalZ=intersz - spherehit.cz;   //diffuse calculation: based on the angle theta (the angle between ray direction and surface normal at intersection) double cost = tAlgebra.GetCosAngleV1V2(lvx, lvy, lvz, vNormalX, vNormalY, vNormalZ);   double vReflX = 0, vReflY = 0, vReflZ = 0; double vEye2IntersX = px - intersx, vEye2IntersY = py - intersy, vEye2IntersZ = pz - intersz; tAlgebra.Reflect(lvx,lvy,lvz, vNormalX,vNormalY,vNormalZ,ref vReflX, ref vReflY, ref vReflZ); // specular calculation: based on the angle phi (the angle between viewing direction and reflected ray direction) double cosf = tAlgebra.GetCosAngleV1V2(vReflX, vReflY, vReflZ, vEye2IntersX, vEye2IntersY, vEye2IntersZ);   Anyway, i have applied some rotation to the final points in some shots   Anderson J. Almeida Systems Analyst SimSysBr
 Re: Specular Highlight efi_germany 3-Aug-07 10:24
 Re: Specular Highlight andalmeida 3-Aug-07 12:38
 Re: Specular Highlight andalmeida 10-Aug-07 6:34
 nice one Amar Chaudhary 26-Jul-07 14:45
 Re: nice one andalmeida 29-Jul-07 4:57
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