Download presentation

Presentation is loading. Please wait.

1
**OpenGL Computer Graphics**

Programming with Transformations

2
**Topics Transformations in OpenGL Saving Current Transformation**

Drawing 3D Scenes with OpenGL OpenGL Functions for Modeling and Viewing

3
**Transformations in OpenGL**

CT: current transformation Simplified graphics pipeline OpenGL maintains so-called modelview matrix Every vertex passed down the graphics pipeline is multiplied by this matrix V Q Window-to-Viewport Transformation S CT S V Q Viewport World Window Screen Coordinate System Model (Master) Coordinate System World Coordinate System

4
**Transformations in OpenGL**

OpenGL is a 3D graphics package Transformations are 3D How does it work in 2D? 2D drawing is done in the xy-plane, z coordinate is 0. Translation: dz = 0 Scaling: Sz = 1 Rotation: z-roll y z x

5
**Transformations in OpenGL**

Fundamental Transformations Translation: glTranslated(dx, dy, dz) for 2D: glTranslated(dx, dy, 0) Scaling: glScaled(sx, sy, sz) for 2D: glScaled(sx, sy, 1.0) Rotation: glRotated(angle, ux, uy, uz) for 2D: glRotated(angle, 0, 0, 1) Transformations does not set CT directly, a matrix is postmultiplied to CT CT = CT M

6
**Transformations in OpenGL**

Canvas functions void Canvas:: initCT(void) { glMatrixMode(GL_MODELVIEW); glLoadIdentity(); } void Canvas:: scale2D(double sx, double sy) glScaled(dx, dy, 1.0);

7
**Transformations in OpenGL**

Canvas functions void Canvas:: translate2D(double dx, double dy) { glMatrixMode(GL_MODELVIEW); glTranslated(dx, dy, 0); } void Canvas:: rotate2D(double angle) glRotated(angle, 0.0, 0.0, 1.0);

8
**Transformations Example**

Draw a house. Draw another house by rotating it through -30° and then translating it through (32, 25) cvs.initCT(); house(); cvs.translate2D(32, 25); cvs.rotate2D(-30.0);

9
**Transformations Example**

10
**Transformations Example**

Think of it in two different ways Q =T(32, 25)R(-30)P CT = CT T(32, 25) R(-30) Translate the coordinate system through (32, 25) and then rotate it through –30° The code generated by these two ways is identical.

11
**Saving Current Transformation**

We can save and restore CTs using glPushMatrix() and glPopMatrix() Manipulation of a stack of CT After rotate2D() After popCT() Before After pushCT() CT4 CT = CT3 Rot CT3 CT3 CT3 CT3 CT2 CT2 CT2 CT2 CT1 CT1 CT1 CT1

12
**Saving Current Transformation**

Canvas functions void Canvas:: pushCT(void) { glMatrixMode(GL_MODELVIEW); glPushMatrix(); } void Canvas:: popCT(void) glPopMatrix();

13
Saving CT Examples Master coordinate system: where an object is defined Modeling transformation: transforms an object from its master coordinate system to world coordinate system to produce an instance Instance: a picture of an object in the scene

14
**Drawing 3D Scenes with OpenGL**

The concept of “camera” (eye) is used for 3D viewing Our 2D drawing is a special case of 3D drawing far plane y view volume near plane z x eye Viewport window

15
**Drawing 3D Scenes with OpenGL**

Camera to produce parallel view of a 3D scene

16
**Drawing 3D Scenes with OpenGL**

Simplified OpenGL graphics pipeline VM P clip Vp modelview matrix projection matrix viewport matrix

17
**Drawing 3D Scenes with OpenGL**

Modelview matrix = CT Object transformation + camera transformation Applying model matrix M then viewing matrix V

18
**Drawing 3D Scenes with OpenGL**

Projection matrix Shifts and scales view volume into a standard cube (extension from –1 to 1) Distortion can be compensated by viewport transformation later

19
**Drawing 3D Scenes with OpenGL**

Viewport matrix Maps surviving portion of objects into a 3D viewport after clipping is performed Standard cube block w/ x and y extending across viewport and z from 0 to 1

20
**OpenGL Modeling and Viewing Functions**

Modeling transformation Translation: glTranslated(dx, dy, dz) Scaling: glScaled(sx, sy, sz) Rotation: glRotated(angle, ux, uy, uz) Camera for parallel projection glMatrixMode(GL_PROJECTION); glLoadIdentity(); glOrtho(left, right, bottom, top, near, far) Example near=2: near plane is 2 units in front of eye far=20: far plane is 20 units in front of eye

21
**OpenGL Modeling and Viewing Functions**

Positioning and aiming camera glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glutLookAt(eye.x, eye.y, eye.z, // eye position look.x, look.y, look.z, // look at point up.x, up.y, up.z) // up vector Up vector is often set to (0, 1, 0) glutLookAt() builds a matrix that converts world coordinates into eye coordinates.

22
**Set up a Typical Camera - Example**

glMatrixMode(GL_PROJECTION); glLoadIdentity(); glOrtho(-3.2, 3.2, -2.4, 2.4, 1, 50) glMatrixMode(GL_MODELVIEW); glutLookAt(4, 4, 4, 0, 1, 0, 0, 1, 0) (4, 4, 4) (0, 1, 0)

23
**Transformation Matrix for LookAt**

Camera coordinate system Axes: u, v, n n = eye – look u = up n v = n u Origin: eye (looking in the direction –n) Transformation matrix

24
**Transformation Matrix for LookAt**

25
**Elementary 3D Shapes Provided by OpenGL**

Cube glutWireCube(GLdouble size) size = length of a side Sphere glutWireSphere(GLdouble radius, GLint nSlices, GLint nStacks) Approximated by polygonal faces nSlices = #polygons around z-axis nStacks = #bands along z-axis

26
**Elementary 3D Shapes Provided by OpenGL**

Torus glutWireTorus(GLdouble inRad, GLdouble outRad, GLint nSlices, GLint nStacks) Approximated by polygonal faces Teapots glutWireTeapot(GLdouble size) There are solid counterparts of the wire objects

27
**Plantonic Solids Provided by OpenGL**

Tetrahedron glutWireTetrahedron() Octahedron glutWireOctahedron() Dodecahedron glutWireDodecahedron() Icosahedron glutWireIcosahedron() All of them are centered at the origin

28
**Plantonic Solids Provided by OpenGL**

29
**Cone Provided by OpenGL**

glutWireCone(GLdouble baseRad, GLdouble height, GLint nSlices, GLint nStacks) Axis coincides with the z-axis Base rests on xy-plane and extends to z = height baseRad: radius at z = 0

30
**Tapered Cylinder Provided by OpenGL**

gluCylinder(GLUquadricObj *qobj, GLdouble baseRad, GLdouble topRad, GLdouble height, GLint nSlices, GLint nStacks) Axis coincides with the z-axis Base rests on xy-plane and extends to z = height baseRad: radius at z = 0 topRad: radius at z = height

31
**Tapered Cylinder Provided by OpenGL**

A family of shapes distinguished by the value of topRad To draw, we have to Deifne a new quadric object Set drawing style GLU_LINE: wire frame GLU_FILL: solid rendering Draw the object

32
**Tapered Cylinder Provided by OpenGL**

Example – wire frame cylinder GLUquadricObj *qobj; qobj = gluNewQuadric(); gluQuadricDrawStyle(qobj, GLU_LINE); gluCylinder(qobj, baseRad, topRad, height, nSlices, nStacks);

35
**#include <gl/glut.h>**

//<<<<<<<<<<<<<<<<<<< axis >>>>>>>>>>>>>> void axis(double length) { // draw a z-axis, with cone at end glPushMatrix(); glBegin(GL_LINES); glVertex3d(0, 0, 0); glVertex3d(0,0,length); // along the z-axis glEnd(); glTranslated(0, 0,length -0.2); glutWireCone(0.04, 0.2, 12, 9); glPopMatrix(); }

36
//<<<<<<<<<<<<<< displayWire >>>>>>>>>>>>>> void displayWire(void) { glMatrixMode(GL_PROJECTION); // set the view volume shape glLoadIdentity(); glOrtho(-2.0*64/48.0, 2.0*64/48.0, -2.0, 2.0, 0.1, 100); glMatrixMode(GL_MODELVIEW); // position and aim the camera gluLookAt(2.0, 2.0, 2.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); // to obtain the picture shown in Figure 5.59 we have to // change the eye location as follows // gluLookAt(1.0, 1.0, 2.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);

37
**glClear(GL_COLOR_BUFFER_BIT); // clear the screen**

glColor3d(0,0,0); // draw black lines axis(0.5); // z-axis glPushMatrix(); glRotated(90, 0, 1, 0); axis(0.5); // x-axis glRotated(-90, 1, 0, 0); axis(0.5); // y-axis glPopMatrix(); glTranslated(0.5, 0.5, 0.5); // big cube at (0.5, 0.5, 0.5) glutWireCube(1.0);

38
glPushMatrix(); glTranslated(1.0,1.0,0); // sphere at (1,1,0) glutWireSphere(0.25, 10, 8); glPopMatrix(); glTranslated(1.0,0,1.0); // cone at (1,0,1) glutWireCone(0.2, 0.5, 10, 8); glTranslated(1,1,1); glutWireTeapot(0.2); // teapot at (1,1,1)

39
glPushMatrix(); glTranslated(0, 1.0 ,0); // torus at (0,1,0) glRotated(90.0, 1,0,0); glutWireTorus(0.1, 0.3, 10,10); glPopMatrix(); glTranslated(1.0, 0 ,0); // dodecahedron at (1,0,0) glScaled(0.15, 0.15, 0.15); glutWireDodecahedron();

40
glPushMatrix(); glTranslated(0, 1.0 ,1.0); // small cube at (0,1,1) glutWireCube(0.25); glPopMatrix(); glTranslated(0, 0 ,1.0); // cylinder at (0,0,1) GLUquadricObj * qobj; qobj = gluNewQuadric(); gluQuadricDrawStyle(qobj,GLU_LINE); gluCylinder(qobj, 0.2, 0.2, 0.4, 8,8); glFlush(); }

41
//<<<<<<<<<<<<<<<< main >>>>>>>>>>>>>>>> void main(int argc, char **argv) { glutInit(&argc, argv); glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB ); glutInitWindowSize(640,480); glutInitWindowPosition(100, 100); glutCreateWindow("Transformation testbed - wireframes"); glutDisplayFunc(displayWire); glClearColor(1.0f, 1.0f, 1.0f,0.0f); // background is white glViewport(0, 0, 640, 480); glutMainLoop(); }

Similar presentations

OK

Drawing 3D Scenes in OpenGL We want to transform objects in order to orient and position them as desired in a 3D scene. OpenGL provides the necessary functions.

Drawing 3D Scenes in OpenGL We want to transform objects in order to orient and position them as desired in a 3D scene. OpenGL provides the necessary functions.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on supply chain mechanism Ppt on area of parallelogram and triangle for class 9 File type ppt on cybercrime laws Ppt on earth movements and major landforms of the united Ppt on india and the great depression Ppt on radio network controller Ppt on atomic structure for class 8 Ppt on two point perspective room Ppt on condition based maintenance technologies Ppt on accounting standards 10