Projections

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Projections
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Viewports

• Windows can have separate viewports
• void glViewport(GLint x,
• GLint y,
• GLsizei width,
• GLsizei height )
• x, y - Specify the lower left corner of the
  viewport rectangle, in pixels
• width, height - Specify the width and height of
  the viewport

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Viewport Example

• Create two viewports in one window
• wWindow width
• hWindow height

//Left Viewport glViewport(0.0,0.0,w/2.0,h) glMat
rixMode(GL_PROJECTION) glLoadIdentity() glOrtho(
-w/4.0,w/4.0,-h/2.0,h/2.0,-1.0,1.0) glMatrixMode(
GL_MODELVIEW) //Draw the scene drawScene() //Ri
ght Viewport glViewport(w/2.0,0.0,w/2.0,h) glMatr
ixMode(GL_PROJECTION) glLoadIdentity() glOrtho(-
w/4.0,w/4.0,-h/2.0,h/2.0,-1.0,1.0) glMatrixMode(G
L_MODELVIEW) //Draw the scene drawScene()
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Projections

• Flattening a 3D virtual scene by projecting it
  onto a plane
• The projected geometry is next rasterized into
  fragments

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View Frustum

• Frustum
• A portion of a solid, normally a cone or pyramid,
  which lies between two parallel planes cutting
  the solid.
• We are interested in Square frusta
• Used to define the viewing volume

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Near and Far Clipping Planes

• Near and Far clipping planes
• Clip out geometry outside of them
• This Geometry is not rendered

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Orthographic Example

• void glOrtho(GLdouble left,
• GLdouble right,
• GLdouble bottom,
• GLdouble top,
• GLdouble nearVal,
• GLdouble farVal)

//Left Viewport glViewport(0.0,0.0,w,h) glMatrixM
ode(GL_PROJECTION) glLoadIdentity() glOrtho(-w/4
.0,w/4.0,-h/2.0,h/2.0,0.0,1.0) //Draw the
scene glMatrixMode(GL_MODELVIEW) drawScene()

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Perspective Example

• void glFrustum( GLdouble left,
• GLdouble right,
• GLdouble bottom,
• GLdouble top,
• GLdouble nearVal,
• GLdouble farVal)

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Perspective Example

• Defined in GL/glu.h
• void gluPerspective(GLdouble fovy,
• GLdouble aspect,
• GLdouble zNear,
• GLdouble zFar )?

//Left Viewport glViewport(0.0,0.0,w,h) glMatrixM
ode(GL_PROJECTION) glLoadIdentity() gluPerspecti
ve(45.0,w/h,1.0,20.0) //Draw the
scene glMatrixMode(GL_MODELVIEW) drawScene()

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Model -gt View -gt Projection

• Modeling Transformation
• Used to position geometry in the scene
• Viewing Transformation
• Used to position and orient the view of a scene
• Projection Transformation
• Used to project a scene onto a viewing plane

glVertex
Modeling Transformation
View Transformation
Projection Transformation
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Setting up the view

• Used to position and orient the view of a scene
• Viewing transformation can be thought of as a
  camera viewing the scene
• Order of transformations that setup a camera
• Position
• Orientation

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gluLookAt

• Defined in ltgl/glu.hgt
• void gluLookAt(
• GLdouble eyeX,
• GLdouble eyeY,
• GLdouble eyeZ,
• GLdouble centerX,
• GLdouble centerY,
• GLdouble centerZ,
• GLdouble upX,
• GLdouble upY,
• GLdouble upZ )?

• eyeX, eyeY, eyeZ
• Specifies the position of the eye point.
• centerX, centerY, centerZ
• Specifies the position of the reference point.
• upX, upY, upZ
• Specifies the direction of the up vector.

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gluLookAt continued

• eyeX, eyeY, eyeZ
• Specifies the position of the eye point.
• centerX, centerY, centerZ
• Specifies the position of the reference point.
• upX, upY, upZ
• Specifies the direction of the up vector.

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Depth Buffer

• Additional component of the frame buffer
• Holds the depth value of each fragment
• Needs to be cleared like color buffer

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Setting up Depth Test

• OpenGL disables depth test by default
• glEnable(GL_DEPTH_TEST)
• We have an additional part of the frame buffer
  that needs clearing
• glClear(GL_COLOR_BUFFER_BIT GL_DEPTH_BUFFER_BIT)
  
• We need a drawing context that has a depth buffer
• glutInitDisplayMode(GLUT_RGBA GLUT_SINGLE
  GLUT_DEPTH)

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Depth Test Example
Display code
GLUT initialization
void display(void)? glEnable(GL_DEPTH_TEST)
glClear(GL_COLOR_BUFFER_BIT
GL_DEPTH_BUFFER_BIT) //Setup state to start
drawing glBegin(GL_TRIANGLES)
glVertex3i(-100, 100, 1) glVertex3i(0,
100, 1) glVertex3i(-50, 50, 1)
glVertex3i(50, 50, 3) glVertex3i(100,
100, 3) glVertex3i(75, 20, 3)
glEnd()
int main(int argc, char argv)?
glutInit(argc, argv) glutInitDisplayMode(GLUT
_RGBA GLUT_SINGLE GLUT_DEPTH)
glutCreateWindow("Depth Example")
glutDisplayFunc(display) glutReshapeFunc(reshap
e) glutMainLoop() return 0