Advanced Solid Shapes in OpenGL for COS 397: Prism, Truncated Cone, and Library Updates

1. COS 397 Computer Graphics Practical Session №3 Solid Shapes

2. Outline • Task 1:Updated Library for COS397 • Task 2:Prism • Task 3:Truncated Cone • Task 4:Pencil

3. Task №1 • We are going to use user defined library • COS397.cpp • COS397.h • You need to copy these files in your project folder and to attach them to the project • In main file should be included by • #include <COS397.h>

4. Modifications in void init() • glfwOpenWindow( 640, 480, 0, 0, 0, 0, 8, 0, GLFW_WINDOW) • This value sets the depth buffer. • It should be greater than 0, and depends on graphical card properties. • Some often used values: 8, 16, 32 …

5. Cube • Side from X– • Has vertices glVertex(x–a,y±a,z±a)alternating signs ± (–,–) → (–,+) → (+,+) → (+,–) –,+ +,+ –,– +,–

6. Cube’s sides: • fromX–glVertex(x–a,y±a,z±a) • fromX+glVertex(x+a,y±a,z±a) • fromY–glVertex(x±a,y–a,z±a) • fromY+glVertex(x±a,y+a,z±a) • fromZ–glVertex(x±a,y±a,z–a) • fromZ+glVertex(x±a,y±a,z+a)

7. Normal Vectors • Normal vectors • Axis Oriented • For sideX+ • glNormal3f(1,0,0) • For sideZ– • glNormal3f(0,0,-1)

8. Lightening • Enabling three settings • General lightening enabling • glEnable( GL_LIGHTING ) • Using the object color in lightening glEnable( GL_COLOR_MATERIAL ) • Turning on one light source (numbering starts from 0)glEnable( GL_LIGHT0 )

9. Circle • Approximated by prism with N>30 • Vertex coordinates • Angle α, in range • Step • Vertex coordinates for polygon

10. Circle • Parallel to OXY: • Parallel to OXZ: • Parallel to OYZ:

11. Cone • For circle approximation of the base we use polygon with N sides • Generatenhorizontal andn vertical triangles (x,y,z+h) (0,0,h) Cone in point (0,0,0) Cone in point (x,y,z) (x,y,z) (0,0,0) (x+x2, y+y2, z) (x2, y2,0) (x+x1, y+y1, z) (x1, y1,0)

12. Cylinder • Like cone with slight modifications (0,0,h) (x,y,z+h) (x+x2, y+y2, z+h) (x2, y2, h) (x1, y1, h) (x+x1, y+y1, z+h) Cylinder in point (0,0,0) Cylinder in point (x,y,z) (0,0,0) (x,y,z) (x+x2, y+y2, z) (x2, y2, 0) (x1, y1, 0) (x+x1, y+y1, z)

13. Solid cylinder • Lightening • Normal vectors for sides • Normal vectors should be unit vectors, i.e. with length 1 • For bottom base • For tom base • For surface

14. Surface normal vectors calculation α+α α+½α α

15. Solid Cone • Lightening • Global problem – surfacenormal vectors calculation • We use a sphere with radius 1 and center (0,0,0)and calculate vectors from point (0,0,0) to the sphere surface points • We need to calculate two angles

16. Horizontal angle αnorm • Like for cylinder surface • Vertical angle βnorm • More complicated • We use transformation from Spherical to Cartesian coordinate system • sin(βnorm)and cos(βnorm) should be calculated

17. βnorm • Normal vector coordinates B βnorm h M A H βnorm r

18. Result Normal vector

19. Task № 2: Prism • Using functions: • void drawCylinder ( float x, float y, float z, float r, float h ); • Void drawSolidCylinder ( float x, float y, float z, float r, float h ); • Define functions • drawPrism and drawSolidPrism

20. void drawSolidPrism( float x, float y, float z, float r, float h , int n ) • { float alpha = 0.0; • float dalpha = 2*M_PI/n; • for( inti=0; i<n; i++) • { • float dx1 = r*cos(alpha); • float dy1 = r*sin(alpha); • float dx2 = r*cos(alpha+dalpha); • float dy2 = r*sin(alpha+dalpha); • glBegin( GL_POLYGON ); • glNormal3f( cos(alpha+dalpha/2), sin(alpha+dalpha/2), 0 ); • glVertex3f( x+dx1, y+dy1, z ); • glVertex3f( x+dx2, y+dy2, z ); • glVertex3f( x+dx2, y+dy2, z+h ); • glVertex3f( x+dx1, y+dy1, z+h ); • glEnd(); • glBegin( GL_POLYGON ); • glNormal3f( 0, 0, -1 ); • glVertex3f( x, y, z ); • glVertex3f( x+dx1, y+dy1, z ); • glVertex3f( x+dx2, y+dy2, z ); • glEnd(); • glBegin( GL_POLYGON ); • glNormal3f( 0, 0, 1 ); • glVertex3f( x, y, z+h ); • glVertex3f( x+dx1, y+dy1, z+h ); • glVertex3f( x+dx2, y+dy2, z+h ); • glEnd(); • alpha += dalpha; • } • }

21. int main() • { • init(); • glClearColor( 1.0f, 1.0f, 1.0f, 1.0f ); • glEnable( GL_DEPTH_TEST ); • glEnable( GL_LIGHTING ); • glEnable( GL_COLOR_MATERIAL ); • glEnable( GL_LIGHT0 ); • while( running() ) • { • glClear( GL_COLOR_BUFFER_BIT+GL_DEPTH_BUFFER_BIT ); • glRotatef( 0.05, 0.4, -0.2, 0.7); • glColor3ub( 255, 255, 0 ); //yellow • drawSolidPrism( 0, 0, -3, 0.3, 6,6 ); • glfwSwapBuffers(); • } • finit(); • return 0; • }

22. Task № 3: Truncated Cone • Using function: • Void drawSolidCone( float x, float y, float z, float r, float h ); • Define function • Void drawTruncatedCone( float x, float y, float z, • float r, float r1, float h ); h r1 r

24. void drawTruncatedCone( float x, float y, float z, float r, float r1, float h ) • { int n = 32; • float h1 = h - h*r1/r; • float alpha = 0.0; • float dalpha = 2*M_PI/n; • for( inti=0; i<n; i++) • { • float dx1 = r*cos(alpha); • float dy1 = r*sin(alpha); • float dx2 = r*cos(alpha+dalpha); • float dy2 = r*sin(alpha+dalpha); • float dx3 = r1*cos(alpha); • float dy3 = r1*sin(alpha); • float dx4 = r1*cos(alpha+dalpha); • float dy4 = r1*sin(alpha+dalpha); • float cosbeta = h/sqrt(h*h+r*r); • float sinbeta = r/sqrt(h*h+r*r); • float nx = cos(alpha+dalpha/2)*cosbeta; • float ny = sin(alpha+dalpha/2)*cosbeta; • float nz = sinbeta; • // surface • glBegin( GL_POLYGON ); • glNormal3f( nx, ny, nz ); • glVertex3f( x+dx1, y+dy1, z ); • glVertex3f( x+dx2, y+dy2, z ); • glVertex3f( x+dx4, y+dy4, z+h1 ); • glVertex3f( x+dx3, y+dy3, z+h1 ); • glEnd(); • // bottom • glBegin( GL_POLYGON ); • glNormal3f( 0, 0, -1 ); • glVertex3f( x, y, z ); • glVertex3f( x+dx1, y+dy1, z ); • glVertex3f( x+dx2, y+dy2, z ); • glEnd(); • //top • glBegin( GL_POLYGON ); • glNormal3f( 0, 0, 1 ); • glVertex3f( x, y, z+h1 ); • glVertex3f( x+dx3, y+dy3, z+h1 ); • glVertex3f( x+dx4, y+dy4, z+h1 ); • glEnd(); • alpha += dalpha; • } }

25. Task № 4: Pencil • Using functions: • drawSolidCylinder , drawSolidPrism, drawTruncatedCone • and drawSolidCone • Define class for compound object Pencil

27. class Pencil{ • private: float s, x,y,z,t; • public: • Pencil(float x1, float y1, float z1, float s1, float t1) • { s = s1; //length • x=x1; • y=y1; • z=z1; • t=t1; //thin • } • void drawPencil() • { • glColor3ub( 225, 200, 0 ); //yellow • drawSolidPrism(x,y,z,t,s,6); • glColor3ub(200, 200, 200 ); //gray • float metal=s/10.0; • drawSolidPrism(x,y,z-metal,t*1.1,metal,18); • glColor3ub(225, 125, 225 ); //pink • float rubber=s/12.0; • drawSolidPrism(x,y,z-metal-rubber,t*0.9,rubber,35); • glColor3ub(250, 215, 145 ); //beige • float wood=s/5.0; • drawTruncatedCone(x,y,z+s,t*0.95,t/3,wood); • glColor3ub(5, 5, 5); //black • float graphite=s/15.0; • drawSolidCone(x,y,z+s+wood-graphite,t/3,graphite); • } • };

28. int main() • { • init(); • Pencil p1 = Pencil(0,0,-3,6,0.3); • glClearColor( 1.0f, 1.0f, 1.0f, 1.0f ); • glEnable( GL_DEPTH_TEST ); • glEnable( GL_LIGHTING ); • glEnable( GL_COLOR_MATERIAL ); • glEnable( GL_LIGHT0 ); • while( running() ) • { • glClear( GL_COLOR_BUFFER_BIT+GL_DEPTH_BUFFER_BIT ); • glRotatef( 0.05, 0.4, -0.2, 0.7); • p1.drawPencil(); • glfwSwapBuffers(); • } • finit(); • return 0; • }

29. Questions?