# 程序代写代做代考 COMP3421

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.

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