Modelling & Representation

Modelling & Representation

Representation of Objects in 3D • Parametric Surface: (R2->R3) • Polygon mesh • High-order surface patch • Implicit: (Solid/Volumetric:R3->0) • implicit • Volxels • CSG

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 coordinates • object= 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

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}}}

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] Example) in Indexed-face Mesh

Draw Methods • Geometric primitives • Begin-end structure • Vertex specifying order • Array • Display 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 using • glEnd(); • Between them you can specify the primitive coordinates, color, normal etc.

Vertex specifying order GL_TRIANGLE_FAN GL_TRIANGLES GL_TRIANGLE_STRIP GL_QUADS GL_QUAD_STRIP

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(); Example

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 lists • Display 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 applications • Vertex 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 primitive glMaterialfv(face, property, value ); • separate materials for front and back

Modelling & Representation