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### l4_post

Course: CS 537, Fall 2009
School: Stevens Institute of...
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Graphics Lecture Computer 4 Transformations Building a Scene GC537 G. Kamberov Today Coordinate systems and transformations The matrix pipeline Modeling: Building a scene Symbols and instancing Hierarchical models Attributes and rendering states (see pages 14 to 32 of the previous lecture.) Animation GC537 G. Kamberov 1 Step by step Construct shapes from geometric primitives, thereby creating...

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Graphics Lecture Computer 4 Transformations Building a Scene GC537 G. Kamberov Today Coordinate systems and transformations The matrix pipeline Modeling: Building a scene Symbols and instancing Hierarchical models Attributes and rendering states (see pages 14 to 32 of the previous lecture.) Animation GC537 G. Kamberov 1 Step by step Construct shapes from geometric primitives, thereby creating mathematical descriptions of objects. Arrange the objects in three dimensional space and select the desired vantage point for viewing the composed scene. Calculate the color of all the objects. The color might be explicitly assigned by the application, determined from specified lighting conditions, or obtained by pasting a texture onto the objects. Convert the mathematical description of objects and their associated color information to pixels on the screen. This process is called rasterization. During these stages, an API might perform other operations, such as eliminating parts of objects that are hidden by other objects. GC537 G. Kamberov The Rendering GC537 G. Kamberov 2 World Coordinates and Model Coordinates GC537 G. Kamberov World Coordinates and Model Coordinates GC537 G. Kamberov 3 Viewing the World GC537 G. Kamberov Viewing Transformation GC537 G. Kamberov 4 MVT, Lights, Material, Shading, Rendering GC537 G. Kamberov Coordinate Systems Object/Model World Camera/eye Image/Normalized View Volume Screen Pixel GC537 G. Kamberov 5 The Transformation Pipeline Modelview Transform Vertex data Projection Transform Perspective division Viewport map Transformations in OpenGL We discussed this in the previous class. Notes TBP Eye coord data GC537 G. Kamberov GC537 G. Kamberov clip coord data Window coordinates NDC 6 Modeling, Scene Graphs GC537 G. Kamberov Possible approaches Symbols and instancing, instancing transforms: can be represented by a table. Hierarchical modeling. Scene graphs (SG). (Scene) Trees DAG GC537 G. Kamberov 7 Symbols & Instances GC537 G. Kamberov Instancing in OpenGL In OpenGL, instancing is created by modifying the model-view matrix: glMatrixMode( GL_MODELVIEW ); glLoadIdentity(); glPushMatrix( ); glTranslatef( ... ); glRotatef( ... ); glScalef( ... ); symbol(); glPopMatrix( ); GC537 G. Kamberov 8 Village code glMatrixMode(GL_MODELVIEW); glLoadIdentity(); setview(); //instance 1 Basic simple house glPushMatrix(); house(); glPopMatrix(); //simple house instance 2 Big house Translated glPushMatrix(); glTranslatef(6, 0, 0); glScalef(2,2,2); house(); glPopMatrix(); //simple house instance 3 Intermed. house Rotated 15deg and Translated glPushMatrix(); glTranslatef(0, 6, 0); glRotated(15, 0,0,1); glScalef(2,1,1); house(); glPopMatrix(); //david house Instance 1 glPushMatrix(); glTranslatef(-6,0,0); glScalef(2,2,2); david_house(); glPopMatrix(); glutSwapBuffers(); GC537 G. Kamberov Hierarchical modeling Objects are grouped hierarchically according to spatial location. Natural for many objects (think of a human body, a car, a city) Locality of reference: important in memory management. Objects of current interest often occur in the same spatial region. SG enable us to eliminate other regions from further processing (important in rendering, collision detection) Persistence issues: saving a scene can be done recursively (each node save itself) The symbol/instance paradigm is like a tree of depth one. GC537 G. Kamberov 9 Trees vs DAG DAG allow high-level sharing of objects but often make the memory costs and code complexity too high. DAGs are natural in many applications, e.g., modeling polygonal meshes where many edges and vertices are shared by higher level objects. GC537 G. Kamberov DAG example: polygonal mesh surface Polygon 1 Polygon 2 Polygon 3 Polygon n Edge 1 Edge 2 Edge 3 Vertex 1 Vertex 2 Vertex 3 GC537 G. Kamberov 10 Hierarchical Modeling and Structures Primitives that can be drawn directly, at leaves Internal node become instances Transformations that position instances of objects label the edges Traverse in pre-order (left to right, depthfirst). Stack based implementation Model independent traversal algorithm GC537 G. Kamberov Example: simple 2D drawing GC537 G. Kamberov 11 Hierarchical modeling: tree of transformations T1.T2.T5.T7.T9(LINE) Final picture, obtained by traversing in pre-order the tree GC537 G. Kamberov Compress the tree If an edge (A,B) is labeled with identity transformation, remove it , and move any drawings from node B into A If edges (A,B) and (A,C) the have same labels, merge the nodes B and C Example: in the previous tree T8 will be removed, and the unit square moved to the parent node GC537 G. Kamberov 12 Model to OpenGL code: Stack based implementation Start from the root, traverse tree in pre-order When visiting a node, if there is a primitive at the node that can be drawn, draw it If going down from a node which has more then one unvisited child, store(push) CTM and attributes before continuing down If coming back up an edge to a node which has unvisited children, pop CTM and attributes Mixes DS with implementation, it is hard wired to the example, dynamic use is clumsy GC537 G. Kamberov The scene glScalef(1.0,-1.0,1.0); //T1 glPushMatrix(); glTranslatef(1.5, 3.0, 0.0); //T2 glScalef(1.0, 2.0, 1.0); //T5 glBegin(GL_LINE_LOOP); //BOX glVertex3f(0.0,0.0,0.0); glVertex3f(1.0,0.0,0.0); glVertex3f(1.0,1.0,0.0); glVertex3f(0.0,1.0,0.0); glEnd(); glTranslatef(0.5,0.0, 0.0); //T7 glRotatef(90.0,0.0,0.0,1.0); //T9 glBegin(GL_LINES); //LINE glVertex3f(0.0,0.0,0.0); glVertex3f(1.0,0.0,0.0); glEnd(); glPopMatrix(); glPushMatrix(); glTranslatef(2.0,1.0,0.0); //T3 glScalef(0.5, 0.5, 1.0); //T6 drawUnitCircle(NUM_SLICES); glPopMatrix(); glScalef(4.0,5.0,1.0); // T4 glBegin(GL_LINE_LOOP); // BOX glVertex3f(0.0,0.0,0.0); glVertex3f(1.0,0.0,0.0); glVertex3f(1.0,1.0,0.0); glVertex3f(0.0,1.0,0.0); glEnd(); glFlush(); GC537 G. Kamberov 13 Model independent traversal algorithm All information is stored in the nodes: (Pointer to a) drawing function Transformation positioning the node w/r to its parent (the local transform matrix LTM) Pointer to right sibling Pointer(s) to child(ren) Attributes color, shading info, bounding volume,. State nodes and scene graphs (see later) GC537 G. Kamberov Tree node typedef struct treenode { GLfloat m[16]; GLfloat clr[3]; int display_list_id; //dspl_lst drawing the node (may use pointer to a fnctn instead) struct treenode *child; struct treenode *sibling; } treenode; GC537 G. Kamberov 14 Traversal function void traverse(treenode* root) { if (root==NULL) return; glPushMatrix(); glPushAttrib(GL_COLOR); glMultMatrixf(root->m); glColor3f((root->clr)[0],(root->clr)[1],(root->clr)[2]); glCallList(root->display_list_id); //drawing function if(root->child != NULL) traverse(root->child); glPopMatrix(); glPopAttrib(); if(root->sibling != NULL) traverse(root->sibling); } GC537 G. Kamberov Display function void display() { glClear(GL_COLOR_BUFFER_BIT); glLoadIdentity(); traverse(&root_node); glFlush(); } GC537 G. Kamberov 15 Basic tasks Set up the tree Define the nodes in particular drawing primitives Easy to implement dynamic construction/destruction of nodes using poi...

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