*This page was last updated: February 17, 2017*

The goals of this project are to use displacement mapping to turn a simple shape into a more interesting one, re-compute its normals, bump-map it, and light it.

The turnin for this project will be all of the source files and a PDF report containing:

- What you did and explaining why it worked this way
- Side-by-side images showing different values for A, B, C, and D.
- Per-fragment lighted mage(s) showing that your normal computation is correct.
- Per-fragment lighted mage(s) showing that your bump-mapping is correct.

This needs to be a PDF file turned into **Teach** with your other files.
Be sure to keep your PDF outside your .zip file so I can gather up all the PDF files at once with a script.

This shape is a decaying cosine wave like this:

The surface spreads across X and Y, rising in Z according to:

**Z = A * cos(2πBr+C) * e ^{-Dr}**

where:

Unlike RenderMan, GLSL has no *calculatenormal( )* function to make
displacement mapping go easier.
So, you have to do it yourself.
But, in this case, it's not too hard.

Remember that the cross product of two vectors gives you a third vector
that is perpendicular to both.
So, all you have to do to get the normal is determine 2 vectors that lie on the surface
at the point in question
(these are called *tangent lines*)
and then take their cross product, and then normalize it.

Each tangent is determined by taking calculus derivatives:

**
float r = x*x + y*y;
float drdx = 2.*x;
float dzdx = -A*sin(2.*π*B*r+C) * 2.*π*B*drdx * exp(-D*r) + A*cos(2.*π*B*r+C) * exp(-D*r) * -D*drdx;
**

and

float dzdy = -A*sin(2.*π*B*r+C) * 2.*π*B*drdy * exp(-D*r) + A*cos(2.*π*B*r+C) * exp(-D*r) * -D*drdy;

The tangent vectors are then formed like this:

**vec3 Tx = vec3(1., 0., dzdx )**

and

**vec3 Ty = vec3(0., 1., dzdy )**

The normal is then formed like this:

**vec3 normal = normalize( cross( Tx, Ty ) );**

Start with the lighting shader we looked at in class. Feel free to use it as-is or as a starting point, or feel free to make your own. At a minumim, you must be able to adjust Ka, Kd, Ks, shininess, and the light position.

##OpenGL GLIB Perspective 70 LookAt 0 0 3 0 0 0 0 1 0 Vertex decaying.vert Fragment decaying.frag Program Decaying \ uA <-0.5 0.00 0.5> \ uB <0.0 2.0 5.0> \ uC <0.0 0.0 12.56> \ uD <0. 0. 5.> \ uNoiseAmp <0.0 0. 5.> \ uNoiseFreq <0.1 1. 5.> \ uKa <0. 0.1 1.0> \ uKd <0. 0.6 1.0> \ uKs <0. 0.3 1.0> \ uShininess <1. 10. 50.> \ uLightX <-20. 5. 20.> \ uLightY <-20. 10. 20.> \ uLightZ <-20. 20. 20.> \ uColor {1. .7 0. 1.} \ uSpecularColor {1. 1. 1. 1.} QuadXY -0.2 1. 200 200

Note that you need to break the quad down into many sub-quads (the "200 200" above) so that there are enough vertices to create a smooth displacement function. Basically you are doing your own microfaceting.

You've determined the normal. Now you want to perturb it in a seemingly random, yet coherent, way. Sounds like a job for noise, right?

Use the glman noise capability to get two noise values. These will be treated as an angle to rotate the normal about x and an angle to rotate the normal about y. Create at least two more sliders: uNoiseAmp and uNoiseFreq.

vec4 nvx = texture( Noise3, uNoiseFreq*vMC ); float angx = nvx.r + nvx.g + nvx.b + nvx.a - 2.; angx *= uNoiseAmp; vec4 nvy = texture( Noise3, uNoiseFreq*vec3(vMC.xy,vMC.z+0.5) ); float angy = nvy.r + nvy.g + nvy.b + nvy.a - 2.; angy *= uNoiseAmp;

Rotate the normal like this:

vec3 RotateNormal( float angx, float angy, vec3 n ) { float cx = cos( angx ); float sx = sin( angx ); float cy = cos( angy ); float sy = sin( angy ); // rotate about x: float yp = n.y*cx - n.z*sx; // y' n.z = n.y*sx + n.z*cx; // z' n.y = yp; // n.x = n.x; // rotate about y: float xp = n.x*cy + n.z*sy; // x' n.z = -n.x*sy + n.z*cy; // z' n.x = xp; // n.y = n.y; return normalize( n ); }

Feature | Points |
---|---|

Correctly show the effect of changing A | 20 |

Correctly show the effects of changing B and C | 20 |

Correctly show the effect of changing D | 20 |

Use lighting to show that you have computed the normal correctly | 20 |

Use lighting to show that you have computed the bump-mapping correctly | 20 |

Potential Total | 100 |