Modelling & Representation

Representation of Objects in 3D

Parametric Surface: (R2->R3)Polygon mesh High-order surface patch

Implicit: (Solid/Volumetric:R3->0) implicit VolxelsCSG

Polygon Mesh

must be convex better be planar or triangulation is required can be represented either be a loop of vertices

or edges mostly be a loop of vertices

the order can be either clockwise or counter-clockwise

two popular representations polygon soup indexed-face mesh

Polygon Soup

face = a list of vertex coordinatesobject= a list of faces

Indexed-face Mesh

All vertex coordinates are placed in an array

Faces = a list of indices to the vertex coordinate array

Objects=a list of such indexed faces

Example

X Z

Y

V4 (-1,0,0)

V1 (0,1,0)

V5 (0,0,-1)

V3 (0,0,1)

V2 (1,0,0)

Example) in Polygon Soup

Pyramid={{{0,1,0},{0,0,1},{1,0,0}},...,{{0,0,1},{-1,0,0},{0,0,-1},{1,0,0}}}

Example) in Indexed-face Mesh

V1 (0,1,0) V[0]

V2 (1,0,0) V[1]

V3 (0,0,1) V[2]

V4 (-1,0,0) V[3]

V5 (0,0,-1) V[4]

F1 (v1,v3,v2)(0,2,1) F[0]

F2 (v1,v4,v3)(0,3,2) F[1]

F3 (v1,v5,v4)(0,4,3) F[2]

F4 (v1,v2,v5)(0,1,4) F[3]

F5 (v3,v4,v5)(2,3,4) F[4]

F6 (v2,v3,v5)(1,2,4) F[5]

Draw Methods

Geometric primitivesBegin-end structureVertex specifying order

ArrayDisplay List

Geometric primitives

GL_POINTS: Individual points GL_LINES: Vertices pairs, individual line segments GL_LINE_STRIP GL_LINE_LOOP GL_TRIANGLES: Vertices triplets interpreted as triangles GL_TRIANGLE_STRIP GL_TRIANGLE_FAN GL_QUADS: Vertices quadruples, 4 sided polygons GL_QUAD_STRIP GL_POLYGON: Boundary of a simple, convex polygon

Begin-end structure

A Primitive is started by glBegin(GLenum mode);

And ended usingglEnd();

Between them you can specify the primitive coordinates, color, normal etc.

Vertex specifying order

GL_TRIANGLE_STRIP

GL_TRIANGLE_FAN

GL_TRIANGLES

GL_QUAD_STRIP GL_QUADS

Example

glBegin(GL_QUADS); glNormal3f(-1, 0, 0); glVertex3d(0.0, 1.0, 0.0);

glVertex3d(0.0, 0.0, 0.0); glVertex3d(0.0, 0.0, -1.0); glVertex3d(0.0, 1.0, -1.0); glNormal3f(0, 1, 0); glVertex3d(0.0, 0.0, 0.0);

glVertex3d(1.0, 0.0, 0.0); glVertex3d(1.0, 0.0, -1.0); glVertex3d(0.0, 0.0, -1.0); glNormal3f(1, 0, 0);

glVertex3d(1.0, 0.0, 0.0); glVertex3d(1.0, 1.0, 0.0); glVertex3d(1.0, 1.0, -1.0); glVertex3d(1.0, 0.0, -1.0);

glEnd();

Display Lists

Create a display list: GLuint id; void init( void ){

id = glGenLists( 1 ); glNewList( id, GL_COMPILE ); … glEndList();

} Call a created list:

void display( void ){ glCallList( id );

}

Display Lists

Not all OpenGL routines can be stored in display lists

State changes persist, even after a display list is finished

Display lists can call other display listsDisplay lists are not editable, but you can

fake it make a list (A) which calls other lists (B, C, and D) delete and replace B, C, and D, as needed

Vertex Arrays

Enable the client states: glEnableClientState( GL_VERTEX_ARRAY )

Setup the pointers: Vertex array :glVertexPointers() Color array:glColorPointers() Normal array:glNormalPointers()

Draw with the arrays: glDrawArrays( GL_TRIANGLE_STRIP, 0, numVerts );

void glDrawElements(GLenum mode,GLsizei count,GLenum type,const GLvoid *indices);

glEnableClientState()

void glEnableClientState( GLenum array ); Parameters

array A symbolic constant for the array you want to enable or disable. This parameter can assume one

of the following values: GL_COLOR_ARRAY

If enabled, use color arrays with calls to glArrayElement, glDrawElements, or glDrawArrays. See also glColorPointer.

GL_EDGE_FLAG_ARRAY If enabled, use edge flag arrays with calls to glArrayElement, glDrawElements, or glDrawArrays. See also

glEdgeFlagPointer. GL_INDEX_ARRAY

If enabled, use index arrays with calls to glArrayElement, glDrawElements, or glDrawArrays. See also glIndexPointer.

GL_NORMAL_ARRAY If enabled, use normal arrays with calls to glArrayElement, glDrawElements, or glDrawArrays. See also

glNormalPointer. GL_TEXTURE_COORD_ARRAY

If enabled, use texture coordinate arrays with calls to glArrayElement, glDrawElements, or glDrawArrays. See also glTexCoordPointer.

GL_VERTEX_ARRAY If enabled, use vertex arrays with calls to glArrayElement, glDrawElements, or glDrawArrays. See also

glVertexPointer.

glVertexPointer()

The glVertexPointer function defines an array of vertex data. void glVertexPointer( GLint size, GLenum type, GLsizei stride,

GLsizei count, const GLvoid *pointer ); Parameters

size The number of coordinates per vertex. The value of size must be 2, 3, or 4.

type The data type of each coordinate in the array using the following symbolic

constants: GL_SHORT, GL_INT, GL_FLOAT, and GL_DOUBLE. stride

The byte offset between consecutive vertices. When stride is zero, the vertices are tightly packed in the array.

count The number of vertices, counting from the first, that are static.

pointer A pointer to the first coordinate of the first vertex in the array.

glColorPointer()

The glColorPointer function defines an array of colors. void glColorPointer( GLint size, GLenum type, GLsizei stride, GLsizei

count, const GLvoid * pointer ); Parameters

size The number of components per color. The value must be either 3 or 4.

type The data type of each color component in a color array. Acceptable data types are

specified with the following constants: GL_BYTE, GL_UNSIGNED_BYTE, GL_SHORT, GL_UNSIGNED_SHORT, GL_INT, GL_UNSIGNED_INT, GL_FLOAT, or GL_DOUBLE.

stride The byte offset between consecutive colors. When stride is zero, the colors are

tightly packed in the array. count

The number of static colors, counting from the first color. pointer

A pointer to the first component of the first color element in a color array.

glNormalPointer()

The glNormalPointer function defines an array of normals. void glNormalPointer( GLenum type, GLsizei stride, GLsizei

count, const GLvoid *pointer ); Parameters

type The data type of each coordinate in the array using the following

symbolic constants: GL_BYTE, GL_SHORT, GL_INT, GL_FLOAT, and GL_DOUBLE.

stride The byte offset between consecutive normals. When stride is zero, the

normals are tightly packed in the array. count

The number of normals, counting from the first, that are static. pointer

A pointer to the first normal in the array.

glDrawArrays()

The glDrawArrays function specifies multiple primitives to render.

void glDrawArrays( GLenum mode, GLint first, GLsizei count );

Parameters mode

The kind of primitives to render. The following constants specify acceptable types of primitives: GL_POINTS, GL_LINE_STRIP, GL_LINE_LOOP, GL_LINES, GL_TRIANGLE_STRIP, GL_TRIANGLE_FAN, GL_TRIANGLES, GL_QUAD_STRIP, GL_QUADS, and GL_POLYGON.

first The starting index in the enabled arrays.

count The number of indexes to render.

glDrawElements

void glDrawElements( GLenum mode,GLsizei count, GLenum type, const GLvoid *indices );

Parameters mode

The kind of primitives to render. It can assume one of the following symbolic values: GL_POINTS, GL_LINE_STRIP, GL_LINE_LOOP, GL_LINES, GL_TRIANGLE_STRIP, GL_TRIANGLE_FAN, GL_TRIANGLES, GL_QUAD_STRIP, GL_QUADS, and GL_POLYGON.

count The number of elements to be rendered.

type The type of the values in indices. Must be one of GL_UNSIGNED_BYTE, GL_

UNSIGNED_SHORT, or GL_UNSIGNED_INT. indices

A pointer to the location where the indices are stored.

Display Lists & Vertex Arrays

Better performance than immediate mode rendering

Display lists can be shared between multiple OpenGL context reduce memory usage for multi-context

applicationsVertex arrays may format data for better

memory access

Appearance

Color Vertex color: Specified on a per-vertex basis Face color: Specified on a per-primitive basis using

glColor3f(). Must enable color material for color tracking:

glEnable(GL_COLOR_MATERIAL);

Material: AMBIENT DIFFUSE SPECULAR SHININESS

Color format – RGBA

Color format – color index

Material Properties

Define the surface properties of a primitiveglMaterialfv(face, property, value );

separate materials for front and back

GL_DIFFUSE Base color

GL_SPECULAR Highlight Color

GL_AMBIENT Low-light Color

GL_EMISSION Glow Color

GL_SHININESS Surface Smoothness