Hierarchical Modeling: Tree of Transformations, Display Lists and Functions, Matrix and Attribute Stacks,

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1 Hierarchical Modeling: Tree of Transformations, Display Lists and Functions, Matrix and Attribute Stacks, Hierarchical Modeling Hofstra University 1 Modeling complex objects/motion Decompose object hierarchically into parts Model each part in local frame, and use affine transformations to position it at its proper place in the part above it in the hierarchy Hierarchical Modeling Hofstra University 2 1

The pipeline conceptually Construct shapes from geometric primitives Arrange the objects in three dimensional space and select the desired vantage point for viewing the composed scene.

2 The pipeline conceptually Construct shapes from geometric primitives 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. During these stages, an API might perform other operations, such as eliminating parts of objects that are hidden by other objects. Hierarchical Modeling Hofstra University 3 The Rendering Hierarchical Modeling Hofstra University 4 2

3 World Coordinates and Model Coordinates Hierarchical Modeling Hofstra University 5 World Coordinates and Model Coordinates Hierarchical Modeling Hofstra University 6 3

4 Viewing the World Hierarchical Modeling Hofstra University 7 Viewing Transformation Hierarchical Modeling Hofstra University 8 4

5 MVT, Lights, Material, Shading, Rendering Hierarchical Modeling Hofstra University 9 Coordinate Systems Object/Model World Camera/eye Image/Normalized View Volume Screen, Pixel Hierarchical Modeling Hofstra University 10 5

6 CTM=PT*MVT. Current Transformation MVT and PT are usually part of the current state Matrix Stacks in OpenGL Hierarchical Modeling Hofstra University 11 Possible approaches Symbols and instancing, instancing transforms: can be represented by a table. Hierarchical modeling. Scene graphs (SG). (Scene) Trees DAGs Hierarchical Modeling Hofstra University 12 6

Instancing in OpenGL In OpenGL, instancing is created by

GL_MODELVIEW ); glloadidentity(); glpushmatrix( );

.. ); symbol(); glpopmatrix( ); Hierarchical Modeling

7 Instancing in OpenGL In OpenGL, instancing is created by modifying the model-view matrix: glmatrixmode( GL_MODELVIEW ); glloadidentity(); glpushmatrix( ); gltranslatef(... ); glrotatef(... ); glscalef(... ); symbol(); glpopmatrix( ); Hierarchical Modeling Hofstra University 13 Symbols & Instances Hierarchical Modeling Hofstra University 14 7

Village code glmatrixmode(gl_modelview); glloadidentity(); setview(); //instance 1 Basic simple house house(); //simple house instance 2 Big house Translated gltranslatef(6, 0, 0); glscalef(2,2,2);

8 Village code glmatrixmode(gl_modelview); glloadidentity(); setview(); //instance 1 Basic simple house house(); //simple house instance 2 Big house Translated gltranslatef(6, 0, 0); glscalef(2,2,2); house(); //simple house instance 3 Intermed. house Rotated 15deg and Translated gltranslatef(0, 6, 0); glrotated(15, 0,0,1); glscalef(2,1,1); house(); //david house Instance 1 gltranslatef(-6,0,0); glscalef(2,2,2); david_house(); Hierarchical Modeling Hofstra University 15 Hierarchical Modeling 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. Hierarchical Modeling Hofstra University 16 8

9 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 Hierarchical Modeling Hofstra University 17 Hierarchical Modeling using Trees Primitives that can be drawn directly, at leaves Internal nodes become instances Transformations that position instances of objects label the edges Traverse in pre-order (visit parent, visit children left to right). Stack based implementation Model independent traversal algorithm Hierarchical Modeling Hofstra University 18 9

10 Example: simple 2D drawing Hierarchical Modeling Hofstra University 19 Hierarchical modeling: tree of transformations T1.T2.T5.T7.T9(LINE) Final picture, obtained by traversing in pre-order the tree Hierarchical Modeling Hofstra University 20 10

11 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) have the 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 Hierarchical Modeling Hofstra University 21 From the tree model to OpenGL code 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 Hierarchical Modeling Hofstra University 22 11

12 Stack implementation of the compressed tree glscalef(1.0,-1.0,1.0); //T1 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(); gltranslatef(2.0,1.0,0.0); //T3 glscalef(0.5, 0.5, 1.0); //T6 drawunitcircle(num_slices); 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(); Hierarchical Modeling Hofstra University 23 Display Lists Need to draw the display at a rate sufficient to avoid noticeable flicker Hierarchical Modeling Hofstra University 24 12

Display Processor Display processor special purpose, limited instruction set, oriented toward drawing graphics primitives Display memory holds lists of instructions called display lists Display list

13 Display Processor Display processor special purpose, limited instruction set, oriented toward drawing graphics primitives Display memory holds lists of instructions called display lists Display list executed repeatedly at a rate sufficient to avoid flicker Hierarchical Modeling Hofstra University 25 Display Modes Immediate Mode as soon as the program executes a statement that defines a primitive, it is sent to the server Retained Mode define the object once, then put its description in a display list. Redisplayed with a simple function call Reduced network traffic Hierarchical Modeling Hofstra University 26 13

14 OpenGL Display Lists #define BOX 1 glnewlist(box, GL_COMPILE); glbegin(gl_polygon); glcolor3f(0.0, 1.0, 0.0); glvertex2f(-1.0, -1.0); glvertex2f( 1.0, -1.0); glvertex2f( 1.0, 1.0); glvertex2f(-1.0, 1.0); glend( ); glendlist( ); Send list to server but don t display contents GL_COMPILE_AND_EXECUTE This can change the original state and leave it altered glcalllist(box); Hierarchical Modeling Hofstra University 27 Definition and Execution #define BOX 1 glnewlist(box, GL_COMPILE); glpushattrib(gl_all_attrib_bits); glpushmatrix( ); glbegin(gl_polygon); glcolor3f(0.0, 1.0, 0.0); glvertex2f(-1.0, -1.0); glvertex2f( 1.0, -1.0); glvertex2f( 1.0, 1.0); glvertex2f(-1.0, 1.0); glend( ); glpopattrib( ); glpopmatrix( ); glendlist( ); Push and pop attributes and coordinates to the stacks Hierarchical Modeling Hofstra University 28 14

15 Stack implementation of the tree of transformations glscalef(1.0,-1.0,1.0); gltranslatef(1.5, 3.0, 0.0); glscalef(1.0, 2.0, 1.0); glcalllist(box); gltranslatef(0.5,0.0, 0.0); glrotatef(90.0,0.0,0.0,1.0); glbegin(gl_lines); glvertex3f(0.0,0.0,0.0); glvertex3f(1.0,0.0,0.0); glend(); gltranslatef(2.0,1.0,0.0); glscalef(0.5, 0.5, 1.0); drawunitcircle(num_slices); glscalef(4.0,5.0,1.0); glcalllist(box); glflush(); Hierarchical Modeling Hofstra University 29 Example: cart with two wheels Hierarchical Modeling Hofstra University 30 15

16 Example: wheel Model a red wheel of radius WHEEL_RAD, consisting of a circle and two crossed spikes. Primitive components are unit circle and crossed orthogonal spikes of length 2. glnewlist(wheel,gl_compile); glpushattrib(gl_color); // red wheel with WHEEL_RAD glcolor3f(1.0,0.0,0.0); // red glscalef(wheel_rad, WHEEL_RAD, 1.0); // scale to wheel radius glbegin(gl_lines); // cross, each bar length 2 glvertex2f( -1.0, 0.0); glvertex2f(1.0, 0.0); glvertex2f( 0.0, -1.0); glvertex2f( 0.0, 1.0); glend(); drawunitcircle(num_slices); // unit circle glpopattrib(); glendlist(); Hierarchical Modeling Hofstra University 31 Example: rod with 2 fixed wheels Model the cart consisting of two red wheels of radius WHEEL_RAD, positioned at the ends of a green rod of length 2*HALF_AXIS_LENGTH. The two wheels are rotated at different angles. glnewlist(cart,gl_compile); glpushattrib(gl_color); glcolor3f(0.0,1.0,0.0); // green glbegin(gl_lines); // rod glvertex2f(-half_axis_length, 0.0); glvertex2f( HALF_AXIS_LENGTH, 0.0); glend(); gltranslatef(-half_axis_length, 0.0, 0.0); //position front WHEEL at axis glrotatef(th, 0.0,0.0,1.0); // rotate a WHEEL by TH glcalllist(wheel); gltranslatef(half_axis_length, 0.0, 0.0); //position back WHEEL at axis glrotatef(th+incr, 0.0,0.0,1.0); // rotate a WHEEL by TH+INCR glcalllist(wheel); glpopattrib(); glendlist(); Hierarchical Modeling Hofstra University 32 16

17 Example: cart with 2 wheels void display() { glclear(gl_color_buffer_bit); glcalllist(cart); glflush(); } void myinit() { glclearcolor(1.0,1.0,1.0,0.0); glmatrixmode(gl_projection); glloadidentity(); gluortho2d(-225.0, 225.0, -225, 225.0); glmatrixmode(gl_modelview); defineparts(); // WHEEL and CART are display lists defined here, } main(). As usual, negotiate with Windows Sys, register callbacks, run loop to process events Hierarchical Modeling Hofstra University 33 Example: spin the wheels Limitations of display lists Use of functions in drawing instances of objects at tree nodes Continuously keep changing the value of rotation angle for turning a wheel Need of double buffering Hierarchical Modeling Hofstra University 34 17

18 Example: spin the wheels,2 void draw_cart() { glpushattrib(gl_color); glcolor3f(0.0,1.0,0.0); // draw axis in green glbegin(gl_lines); glvertex2f(-half_axis_length,0.0); glvertex2f(half_axis_length,0.0); glend(); gltranslatef(-half_axis_length,0.0, 0.0); // position front wheel at axis, T1 glrotatef(theta,0.0,0.0,1.0); // spin front WHEEL by theta glcalllist(wheel); // draw wheel gltranslatef(half_axis_length,0.0, 0.0); // position back wheel at axis, T2 glrotatef(theta, 0.0,0.0,1.0); // spin back WHEEL by theta glcalllist(wheel); // draw wheel glpopattrib(); } Hierarchical Modeling Hofstra University 35 Open GL interactive program structure int main(int argc, char** argv) { glutinit(&argc,argv); glutinitdisplaymode (GLUT_SINGLE GLUT_RGB); glutcreatewindow( generic example"); myinit (); glutreshapefunc (myreshape); glutmousefunc (mouse); glutmotionfunc(do_on_motion); glutidlefunction(idle); glutdisplayfunc(display); glutmainloop(); } Hierarchical Modeling Hofstra University 36 18

19 Example: spin the wheels,3, the Idle Function void idle(void) // IDLE callback function updates { // rotation angle that spins a wheel theta += INCR_ANGLE; glutpostredisplay(); } void mousemotion(int x, int y) // MOTION callback function updates { // translation vector that moves whole transx = x; transy = y; glutpostredisplay(); } void display() // DISPLAY callback draws whole object { // in back buffer then swaps buffers glclear(gl_color_buffer_bit); // translate whole object axis with spinning wheels gltranslatef( (float)transx, (float)(windowh-transy), 0.0); draw_cart(); } glutswapbuffers(); // SWAP BUFFERS Hierarchical Modeling Hofstra University 37 Example: spin the wheels, 4, the Idle Function int main( ) { glutinitdisplaymode(glut_double GLUT_RGB); // double buffering... glutdisplayfunc(display); glutmotionfunc(mousemotion); glutidlefunc(idle); glutmainloop(); } Hierarchical Modeling Hofstra University 38 19

20 HW: Model hierarchically a 3D scene consisting of a circular road, a car, at least 2 trees along the road. Each component has a different color than the rest. Allow for interactively changing the camera position, allowing the camera to rotate around the horizontal and vertical axis of the coordinate system attached to the scene, and also for interactively choosing an option to move the car forward or backward A car has a rectangular body and 4 wheels A tree has a trunk (cylinder) and a crown (sphere) The road is a circular loop Model each object (object part) in its own local coordinate system; use transformations to position all objects in the scene. Trees of transformations should help in modeling the individual objects (tree, car), and also in putting the whole scene together. Use functions or display lists to model the components HW is due in 2 weeks. Pace yourself well: complete the modeling in a week, so the week after you could deal with the interaction and the animation. Model and test each object individually, first. Hierarchical Modeling Hofstra University 39 Example: model circular road // ROAD_RAD1, ROAD_RAD2, ROAD_SL, ROAD_RINGS defined globally void draw_road() { GLUquadric* q; q = glunewquadric(); // dynamic array to hold vertices of road // creates and returns a ptr to new quadric object glpushattrib(gl_all_attrib_bits); glcolor3f(0.5,0.5,0.5); // road is gray gludisk(q, ROAD_RAD1, ROAD_RAD2, ROAD_SL, ROAD_RINGS); glpopattrib(); } gludeletequadric(q); Hierarchical Modeling Hofstra University 40 20

21 Example: model circular road void display() { glclear(gl_color_buffer_bit); // glrotatef(45,1.0,0.0,0.0); //glulookat(0.0,0.0,0.0, -1.0,-1.0,-1.0, 0.0,0.0,1.0); draw_road(); glflush(); } Hierarchical Modeling Hofstra University 41 21

Computer graphics MN1

Computer graphics MN1 Hierarchical modeling Transformations in OpenGL glmatrixmode(gl_modelview); glloadidentity(); // identity matrix gltranslatef(4.0, 5.0, 6.0); glrotatef(45.0, 1.0, 2.0, 3.0); gltranslatef(-4.0,