Assignment 2 Phase 1

TransformationBack-face culling

View frustum culling

Outline

Implement the transformation. Modelview transformation Projection transformation Perspective division Viewport transformation

Implement back-face culling. Bonus: Implement view frustum culling.

Input and Output

Input: *.view *.obj *.mtl Same as assignment 1

Output: Wireframe of the obj with back-face culling

Transformation 1/3

ModelviewMatrix

ModelviewMatrix

ViewportTransformation

ViewportTransformation

ProjectionMatrix

ProjectionMatrix

PerspectiveDivision

VertexVertex

Vertex = Projection * Modelview * Vertex ;

Vertex.xyzw /= Vertex.w;

Vertex = Viewport * Vertex;

Model view

N = (eye - at)/|eye - at|; V = up – (N•up)N; |up| = 1.0

U = V x N ;

gluLookAt( GLdouble eyex, GLdouble eyey, GLdouble eyez, GLdouble atx, GLdouble aty, GLdouble atz,

GLdouble upx, GLdouble upy, GLdoubpe upz );

Model view

Modelview = BT

Projection gluPerspective( GLdouble fovy, GLdouble aspect, GLdouble near, GLdo

uble far );

Projection

n=near; f=far; t=n*tan( fovy *PI / 180.0 /2); b= -t; r= t* aspect; l= -r;

Projection

Projection = NSH

=

Perspective Division

x /= w; y /= w; z /= w; w /= w;

View Port

Viewport = TS From [-1 , 1 ] to [0 , width (or height) ]

1000

0100

2/010

2/001

height

width

T

1000

0100

002/0

0002/

height

width

S

Back-face culling You can perform

back-face culling in World cord.

View cord.

ZN < 0

Window cord. Clock wise

0NV

Back face

1

3 2

View frustum culling

eliminate the polygon that complete outside the view frustum.

Bonus: view frustum clipping Remove the part of polygon that

outside the view frustum.

How to draw wireframe? Render the image using

glBegin(GL_LINE_LOOP);glVertex2i(x,y);…glEnd();

What to do in reshape function?void GL_reshape(GLsizei w, GLsizei h){

glViewport(viewport->x, viewport->y, viewport->width, viewport->height);

glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D(viewport->x, viewport->width,

viewport->y, viewport->height);glMatrixMode(GL_MODELVIEW);glLoadIdentity();

}

UI requirement

Show an input command line. “Please input the file name.” If I type “box”, then read box.obj and b

ox.view etc.