graphics graphics lab @ korea university kucg.korea.ac.kr viewing 고려대학교 컴퓨터...

Graphics

kucg.korea.ac.kr Graphics Lab @ Korea University

Viewing

고려대학교 컴퓨터 그래픽스 연구실

kucg.korea.ac.kr

KUCG

Graphics Lab @ Korea University

Fundamental Types of Viewing

Perspective views finite COP (center of projection)

Parallel views COP at infinity DOP (direction of projection)

perspective view parallel view

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Parallel View

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Perspective View

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Classical Viewing

Specific relationship between the objects and the viewers

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Orthographic Projections

Projectors are perpendicular to the projection plane preserve both distances and angles

orthographic projections temple and three multiview orthographic projections

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Axonometric Projections (1/2)

Projection plane can have any orientation with respect to the object projectors are still orthogonal to the projection planes

top view side viewconstruction

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Axonometric Projections (2/2)

Preserve parallel lines but not angles isometric – projection plane is placed symmetrically w

ith respect to the three principal faces dimetric – two of principal faces trimetric – general case

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Oblique Projections

Projectors can make an arbitrary angle with the projection plane preserve angels in planes parallel to the projection

plane

top view side viewconstruction

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Perspective Projections (1/2)

Diminution of size when objects are moved father from the viewer, their

images become smaller

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Perspective Projections (2/2)

One-, two-, and three-point perspectives how many of the three principal directions in the

object are parallel to the projection plane vanishing points

three-point perspective

two-point perspective

one-point perspective

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Positioning of the Camera (1/3)

initial configuration after change in the model-view matrix

OpenGL places a camera at the origin of the world frame pointing in the negative z direction move the camera away from the objects

glTranslatef(0.0, 0.0, -d);glTranslatef(0.0, 0.0, -d);

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Look at the same object from the positive x axis translation after rotation by 90 degrees about the y

axis

glMatrixMode(GL_MODELVIEW);glLoadIdentity( );glTranslatef(0.0, 0.0, -d);glRotatef(-90.0, 0.0, 1.0, 0.0);

glMatrixMode(GL_MODELVIEW);glLoadIdentity( );glTranslatef(0.0, 0.0, -d);glRotatef(-90.0, 0.0, 1.0, 0.0);

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Create an isometric view of the cube

y y

)1 ,1 ,1( )2 ,1 ,0(

z

y

1000

02/202/2

0010

02/202/2

1000

03/63/30

03/33/60

0001

1000

100

0010

0001

dyxRTRM

x x

)2 ,1 ,0(

view from positive z axis


view from positive x axis

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Create an isometric view of the cube

glMatrixMode(GL_MODELVIEW);glLoadIdentity( );glTranslatef(0.0, 0.0, -d);glRotatef(35.26, 1.0, 0.0, 0.0);glRotatef(45.0, 0.0, 1.0, 0.0);

glMatrixMode(GL_MODELVIEW);glLoadIdentity( );glTranslatef(0.0, 0.0, -d);glRotatef(35.26, 1.0, 0.0, 0.0);glRotatef(45.0, 0.0, 1.0, 0.0);

x

)3 ,0 ,0(

yy y

)1 ,1 ,1( )2 ,1 ,0(

x x



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U-V-N System (1/2)

VRP (view-reference point), VPN (view-plane normal), and VUP (view-up vector) u, v (up-direction vector), n (normal vector)

x, y, z axes respectively

camera frame determination of the view-up vector

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U-V-N System (2/2)

Translation after rotation VRP – (x, y, z) T(-x, -y, -z) VNP – (nx, ny, nz) n

VUP – vup v = vup – (vup• n) n

u = v n

( our assumption – all vectors must be normalized )※

1000

0

0

0

1000

100

010

001

zyx

zyx

zyx

nnn

vvv

uuu

z

y

x

TRM

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Look-At Function

OpenGL utility function

VRP: eyePoint VPN: – ( atPoint – eyePoint ) VUP: upPoint – eyePoint

gluLookAt(eyex, eyey, eyez, atx, aty, atz, upx, upy, upz);gluLookAt(eyex, eyey, eyez, atx, aty, atz, upx, upy, upz);

look-at positioning

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Others

Roll, pitch, and yaw

ex. flight simulation

Elevation and azimuth ex. star in the sky

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Simple Perspective Projections (1/2) Simple camera

projection plane is orthogonal to z axis projection plane in front of COP

three-dimensional view

top view side view

d

x

z

xdz p

p ,

dz

yy

dz

xx pp /

,/

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Simple Perspective Projections (2/2) Homogeneous coordinates

Perspective projection matrix

w

wz

wy

wx

z

y

x

1

p

dz

z

y

x

dz

zdz

ydz

x

ddz

ydz

x

z

y

x

p

p

p

/1/

/

/

1

/

/

1

p

0/100

0100

0010

0001

d

M

projection pipeline

Model-viewModel-view ProjectionProjection Perspective division

Perspective division

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Simple Orthogonal Projections

Projectors are perpendicular to the view plane

Orthographic projection matrix

0

p

p

p

z

yy

xx

11000

0000

0010

0001

1

z

y

x

z

y

x

p

p

p

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Projections in OpenGL

Angle of view only objects that fit within the

angle of view of the camera appear in the image

View volume be clipped out of scene frustum – truncated pyramid

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Perspective in OpenGL (1/2)

Specification of a frustum

near, far: positive number !!

zmax = – far

zmin = – near

glMatrixMode(GL_PROJECTION);glLoadIdentity( );glFrustum(xmin, xmax, ymin, ymax, near, far);

glMatrixMode(GL_PROJECTION);glLoadIdentity( );glFrustum(xmin, xmax, ymin, ymax, near, far);

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Perspective in OpenGL (2/2)

Specification using the field of view

fov: angle between top and

bottom planes fovy: the angle of view in the

up (y) direction aspect ratio: width divided

by height

glMatrixMode(GL_PROJECTION);glLoadIdentity( );gluPerspective(fovy, aspect, near, far);

glMatrixMode(GL_PROJECTION);glLoadIdentity( );gluPerspective(fovy, aspect, near, far);

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Parallel in OpenGL

Orthographic viewing function

OpenGL provides only this parallel-viewing function near < far !!

no restriction on the sign

zmax = – far

zmin = – near

glMatrixMode(GL_PROJECTION);glLoadIdentity( );glOrtho(xmin, xmax, ymin, ymax, near, far);

glMatrixMode(GL_PROJECTION);glLoadIdentity( );glOrtho(xmin, xmax, ymin, ymax, near, far);

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Walking Though a Scene (1/2)

void display(void){ glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glLoadIdentity(); gluLookAt(viewer[0], viewer[1], viewer[2], 0,0,0, 0,1,0); glRotatef(theta[0], 1.0, 0.0, 0.0); glRotatef(theta[1], 0.0, 1.0, 0.0); glRotatef(theta[2], 0.0, 0.0, 1.0); colorcube( );

glFlush( ); glutSwapBuffers( );}

void keys(unsigned char key, int x, int y){ if(key == ‘x’) viewer[0] -= 1.0; if(key == ‘X’) viewer[0] += 1.0; if(key == ‘y’) viewer[1] -= 1.0; if(key == ‘Y’) viewer[1] += 1.0; if(key == ‘z’) viewer[2] -= 1.0; if(key == ‘Z’) viewer[2] += 1.0;}

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Walking Though a Scene (2/2)

void myReshape(int w, int h){ glViewport(0, 0, w, h);

glMatrixMode(GL_PROJECTION); glLoadIdentity( ); if( w <= h )

glFrustum(-2.0, 2.0, -2.0*(GLfloat)h/(GLfloat)w, 2.0*(GLfloat)h/(GLfloat)w, 2.0, 20.0);

elseglFrustum(-2.0 *(GLfloat)w/(GLfloat)h, 2.0 *(GLfloat)w/(GLfloat)h, -2.0, 2.0, 2.0, 20.0);

glMatrixMode(GL_MODELVIEW);}

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Projections & Shadows (1/2)

Shadow polygon Steps

light source at (xl, yl, zl)

translation (-xl, -yl, -zl)

perspective projection through the origin

translation (xl, yl, zl)

1000

100

010

001

00/10

0100

0010

0001

1000

100

010

001

1

l

l

l

l

l

l

l

z

y

x

y

z

y

x

PTTM

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Projections & Shadows (2/2)

GLfloat m[16]; /* shadow projection matrix */for(i=0; i<16; i++) m[i] = 0.0;m[0] = m[5] = m[10] = 1.0;m[7] = -1.0/yl;

glColor3fv(polygon_color);glBegin(GL_POLYGON);.. /* draw the polygon normally */.glEnd( );

glMatrixMode(GL_MODELVIEW);glPushMatrix( ); /* save state */glTranslatef(xl, yl, zl); /* translate back */glMultMatrixf(m); /* project */glTranslatef(-xl, -yl, -zl); /* move light to origin */glColorfv(shadow_color);glBegin(GL_POLYGON);.. /* draw the polygon again */.glEnd( );glPopMatrix( ); /* restore state */

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Shadows from a Cube onto Ground

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