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Exploring Transformations in Computer Graphics: Gear Modeling and Animation Techniques

This lab focuses on modeling and animating a gear wheel using OpenGL techniques in a computer graphics course. Participants will learn how to draw symmetric objects and create patterns while exploring square and hexagonal tiling. The lab covers generating a gear wheel with multiple teeth through geometric transformations, including scaling and translating for animation. Students will also engage in exercises that involve creating symmetric designs such as snowflakes, emphasizing reflection and repetition in graphics. Gain hands-on experience with essential OpenGL functions and develop skills in visual programming.

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Exploring Transformations in Computer Graphics: Gear Modeling and Animation Techniques

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  1. Transformationsfor Modeling & Animation Open GL Lab 10 BSCS – 514 Computer Graphics Instructor Humera Tariq

  2. Lab Objectives /Tasks • Modeling & Animating Gear Wheel • Drawing Symmetric Object • Making Patterns • Square & Hexagonal Tiling • Next More on Transformations BSCS – 514 Computer Graphics Instructor Humera Tariq

  3. 1. Modeling a gearwheel • Drawing the axes, title and circle are easy • There are 30 teeth. Each is transformed from a basic tooth void tooth0() { glBegin( GL_LINE_STRIP); glVertex2f(0.0, 0.0); glVertex2f(0.2, 0.2); glVertex2f(0.6, 0.2); glVertex2f(0.6, 0.8); glVertex2f(0.2, 0.8); glVertex2f(0.0, 1.0); glEnd(); } 1. .8 .2 .2 .6

  4. To transform the basic tooth to the right tooth on the x axis • In both x and y dimensions, scale down by 2 r sin 6o • Translate the scaled tooth by Tx = rcos 6o ,Ty = -r sin 6o void tooth1( double r) { double rad = 6.0 * 3.1416 / 180.0, sin6 = r * sin( rad), cos6 = r * cos( rad); glPushMatrix(); glTranslatef( cos6, -sin6, 0.0); glScalef( 2.0*sin6, 2.0*sin6, 1.0); tooth0(); glPopMatrix(); } 2 r sin6o (r cos6o,-r sin6o) 6o

  5. r • To draw the entire set of teeth of radius r and centered at the origin void gear( double r) { glPushMatrix(); for (inti=1; i<=30; ++i) { tooth1( r); glRotatef( 12.0, 0.0, 0.0, 1.0); } glPopMatrix(); }

  6. //Standard Setup for animation float speed = 0.0001; static intoldTime = clock(), newTime; newTime = clock(); deg += (newTime - oldTime) * speed; //printf("%d\n",newTime - oldTime); oldTime = newTime; glutPostRedisplay(); • Animation An object will appear moving if we keep redrawing it with minute changes. void move() { }

  7. 2. Drawing Symmetric Object • It is easy to produce a complex snowflake by designing one half of a spoke, and drawing it 12 times. BSCS – 514 Computer GraphicsInstructor Humera Tariq

  8. Snowflake example continued…. • (a) # include “turtle.h” • (b) gluOrtho2D(-10,10,-10,10) • (c) L = 1 ; Implement voidflakeMotif(float L) • (d) Complete one spoke(reflection w.r.t x-axis) • Draw entire snowflake ?????????????????????? BSCS – 514 Computer GraphicsInstructor Humera Tariq

  9. 3. Making Patterns fromdino motif BSCS – 514 Computer Graphics Instructor Humera Tariq

  10. 4. Tiling and its Applications Simple Square Tiling BSCS – 514 Computer Graphics Instructor Humera Tariq

  11. b) a) D H W L Tiling example from book BSCS – 514 Computer Graphics Instructor Humera Tariq

  12. Tiling Code for fig.5.46 cvs.pushCT(); // so we can return here cvs.translate2D(W, H); // position for the first motif for(row = 0; row < 3; row++){ // draw each row pushCT(); for(col = 0 ; col < 3; col++){ motif(); cvs.translate2D(L, 0);} //move to the right cvs.popCT(); // back to the start of this row cvs.translate2D(0, D); }//move up to the next row cvs.popCT(); //back to where we started BSCS – 514 Computer Graphics Instructor Humera Tariq

  13. Tiling Important exercise BSCS – 514 Computer Graphics Instructor Humera Tariq

  14. More on Transformations BSCS – 514 Computer Graphics Instructor Humera Tariq

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