COMP3421
COMP3421
Introduction to 3D Graphics Solutions
Solution
Exercise 1: See code for implementation
glu.gluPerspective(60,1,2,8);
top = near * tan(fov/2)
= 2 * tan(30) = 1.155
bottom = -1.155
Since we have an aspect ratio of 1 the left
and right would be the same,
gl.glFrustum(-1.155,1.155,-1.155,1.155,2,8)
Solution
Since we have not transformed our points,
they are in camera co-ordinates. Our
nearplane N is 2. x* = NPx/-Pz, y* = NPy/-
Pz ,
(2,1,-4) x* = 2*2/4 = 1 y* = 2/4
(0,-1,-3) x* = 2*0/3 = 0 y* = -2/3
(-2,1,-4) x* = 2*-2/4 = -1 y* = -2/4
Solution
Pseudo-depth z* = (aPz+b)/-Pz
a = (F+N)/F-N, b = -2FN/(F-N)
a = (2+8)/(8-2) = 10/6 b = -2*2*8/(6)=-32/6
(2,1,-4) z* = (-10/6*-4-32/6)/4 = 0.333
(0,-1,-3) z* = (-10/6*-3-32/6)/3 = -0.333
(-2,1,-4) z* = 0.333
Solution
We would have to move camera at least by
2 or more in the z direction. Here I have
moved it by 2.5 (exactly 2 may not work as
it may or may still get clipped).
gl.glTranslate(0,0,-2.5); OR
glu.gluLookAt(0,0,2.5,0,0,0,0,1,0);
We could not simply move the near plane
to 0 as this is not valid for a perspective
camera.