6/15/2015©Zachary Wartell 1 OpenGL Transforms with Object-Oriented Framework Revision 1.1 Copyright...

04/18/23©Zachary Wartell 1

OpenGL Transforms with Object-Oriented Framework

Revision 1.1Copyright Zachary Wartell, University of North Carolina at Charlotte, 2008

All Rights Reserved

Reading:- Hearn & Baker - Chapter 5- OpenGL Programming Guide - Chapter 3 –

emphasis on "Manipulating the Matrix Stacks" "Examples of Composing Several Transformations"

OpenGL Modeling Transformations


glBegin (GL_QUADS);glVertex2i(-0.5,-0.5);glVertex2i( 0.5,-0.5);glVertex2i( 0.5, 0.5);glVertex2i(-0.5, 0.5);glEnd();

coordinatesin

objectcoordinate space

coordinatesin eye

coordinate space

coordinatesin

windowcoordinate space

Vertex commands

GL_MODELVIEWmatrix

GL_PROJECTIONmatrix

+glViewport

matrix

MMV = Meye←object = Meye←world Mworld ← object

MP = Mclip←eye …other magic…MVP = Mwin←ndev

2D Example


O

W=E

MMV = Meye←object = Meye←world Mworld ← object

= I · Mworld ← object

View Window (2.5,2.5)W

(-2.5,-2.5)W MP = Mclip←eye - gluOrtho2D

(1,1)Clip

(-1,-1)Clip


Matrix Transform Functions

• glMatrixMode({GL_MODELVIEW,GL_PROJECTION});

• glLoadMatrix[fd] (…)• glLoadIdentity ()

• glTranslate[fd] (…)• glRotate[fd] (…)• glScale[fd] (…)• glMultMatrix[fd] (…)


glMatrixMode(GL_MODELVIEW);

glLoadIdentity();

DrawUnitBox(RED);

glTranslatef(0,1.5,0);

DrawUnitBox(BLUE);

glLoadIdentity();

glTranslatef(0,2.5,0);

glRotatef(45,0,0,1);

DrawUnitBox(GREEN);

glLoadIdentity();

glTranslatef(1.5,2.5,0)

glScalef(0.5,2.0,1);

DrawUnitBox(ORANGE);

Matrix Example

x

y

MMV = I

MMV = MMV • T1

MMV = I

MMV = MMV ·T2

MMV = MMV ·R1

MMV = I

MMV = MMV ·T3

MMV = MMV·S1

I ·

T1 ·

(T2·R1) ·

(T3·S1) ·

(-0.5,-0.5)

( 0.5,0.5)W


Matrix Stack

• OpenGL uses one stack for each matrix mode– all matrix operations alter the top matrix – vertex coordinates transformed by the top

stack – glPushMatrix – push a new matrix onto the

stack; the pushed matrix is a copy of previous stack top

– glPopMatrix – pop the stack


Matrix Stack Operation

glLoadMatrixf (Q);

glTranslate3f(tx,ty,tz);

glScale3f(sx,sy,sz);

glPushMatrix();

glRotatef(90.0,0.0,0.0,1.0);

glPopMatrix();

glTranslate(tx2,ty2,tz2);M0MMV =Q=Q·T1=Q·T1·S1

=Q·T1·S1M1 =Q·T1·S1·R1MMV

=Q·T1·S1·T2


glLoadIdentity();

glTranslatef(2,2,0);

DrawUnitBox(BLUE);

for (angle=0;angle < 360;angle += 90)

{

glPushMatrix();

glRotatef(angle,0,0,1);

glTranslatef(1,0,0);

glScalef(0.5,0.5,1);

DrawUnitBox(RED);

glPopMatrix();

}

Procedure Approach – Hierarchical Objects

x

y

(-0.5,-0.5)

( 0.5,0.5)

W

Object-Oriented Approach (Non-hierarchical)


class PosableBox{Point2 origin;float orientation;float scale[2];

…};

void PosableBox::render() const{glPushMatrix();glTranslatef(origin[0],origin[1],0);glRotatef(orientation,0,0,1);glScalef(scale[0],scale[1],1);DrawUnitBox(BLUE);glPopMatrix();}

x

y

(-0.5,-0.5)

( 0.5,0.5)

W

MMV = TB·RB·SB

draw TB·RB·SB

B

( 0.5,0.5)B, (1.8,2.6)W `

Change of Coordinates – Collision/Boundary Violation



…};


x

y

(-0.5,-0.5)

( 0.5,0.5)

W

MMV = TB·RB·SB

draw TB·RB·SB

B

( 0.5,0.5)B,

MW←B = TB·RB·SB

(1.8,2.6)W

Change of Coordinates – Mouse Click



…};


x

y

(-0.5,-0.5)

( 0.5,0.5)

W

MMV = TB·RB·SB

draw TB·RB·SB

B

( 0.5,0.5)B,

MB←W = ?

MW←B = TB·RB·SB

MB←W = MW←B -1 = (TB·RB·SB) -1

= SB -1 ·RB

-1 ·TB -1

(1.8,2.6)W

(2.3,0.8)W

(0,-0.25)B

Object-Oriented – Hierarchical – Step #1


class CoordinateSystem{Point2 origin;float orientation;float scale[2];

…};

class Shape{ …};

CS1

UB1 UD1 P1

class Polygon : Shape;

attachment

shapes (0..*)

parent (0..1)

class UnitBox : Shape;

class UnitDisc : Shape;

World Coordinates (W)

MW←CS1



void CoordinateSystem::render(){glPushMatrix();…post multiply MWorld←Local onto MMV……call Shape::render on all attached Shapes…glPopMatrix();}

void UnitDisc::render (){…send GL the vertex coordinates describing a unit disc measured in local coordinates …}

CS1

UB1 UD1 P1

x

y

WMMV = MW←CS1=TCS1·RCS1·SCS1

render MW←CS1 ·render MW←CS1 ·render MW←CS1



class CoordinateSystem{Point2 origin;float orientation;float scale[2];

…};

CS1

UB1 UD1 P1

Att

achm

ent

children (0..*)

parent (0..1)

CS2

UB2

MCS1←CS2

MW←CS1


04/18/23 15

void CoordinateSystem::render(){glPushMatrix();…post multiply MParent←Local onto MMV…for all attached Shapes

Shape::renderfor all attached CoordinateSystems

CoordinateSystem::render glPopMatrix();} CS1

UB1 UD1 P1 CS2

UB2

CS3

UD2

MCS1←CS3

MCS1←CS2

MW←CS1

W



void CoordinateSystem::render(){glPushMatrix();…post multiply MParent←Local onto MMV…for all attached Shapes

Shape::renderfor all attached CoordinateSystems

CoordinateSystem::render glPopMatrix();}

MMV =IM0 =I

MMV =I

M0 =I

MMV =I · T CS1 ·R CS1 ·SCS1

MW←CS1M0 =I

M1 =I · T CS1 ·R CS1 ·SCS1

MW←CS1


M0 =I


MW←CS1

MMV =I · T CS1 ·R CS1 ·SCS1· T CS2 ·R CS2 ·SCS2

MCS1←CS2

MW←CS2

M0 =I


MW←CS1M0 =I


MW←CS1


M0 =I


MW←CS1

MMV =I · T CS1 ·R CS1 ·SCS1· T CS3·R CS3 ·SCS3

MCS1←CS3

MW←CS3

M0 =I


MW←CS1MMV =I

CS1

UB1 UD1 P1 CS2

UB2

CS3

UD2

MCS1←CS3

MCS1←CS2

x

y

W

CS1

CS2

CS

3

MW←CS1

W


Tricky BitOpenGL specifications and documents use column-vector notation:

But in C/C++, GL follows the row-major memory organization for matrices:

GLfloat translate[4][4] = {{1, 0, 0, 0}, {0, 1, 0, 0},

{0, 0, 1, 0}, {tx,ty,tz,1}};

When building matrices to transfer to GL or examining matrices retrieved from GL, you must remember the array layout is the transpose of the mathematical convention.

Alternatively, you can use the “transpose” versions of GL matrix routines which accept and return matrix arrays organized using the conventional mathematical layout (see glLoadTransposeMatrix, etc.)

1 0 0

0 1 0

0 0 1

0 0 0 1 1

tx x

ty y

tz z

row column

6/15/2015©Zachary Wartell 1 OpenGL Transforms with Object-Oriented Framework Revision 1.1 Copyright...

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