solve an equation for perspective projection

Hi guys I got an equation need to simplify but am new to simplify command

D^2=(xa-xb)^2+(ya-yb)^2+(Za-Zb)^2

knowing that:

xa=-f*Xa/Za

xb=-f*Xb/Zb

ya=-f*Ya/Za

yb=-f*Yb/Zb

what i want is to simplify the equation to this form :

af^2+bf+c=0

thank you for help in advance regards,

Answer 1

[K]

Hi,

I'm sure this isn't the best solution, but if you enter f, Xa,Xb,Ya,Yb,Za, and Zb as symbols, and then enter your four constraints, and then your equation for D^2, and then use expand, you can pretty easily read off the terms and group them as you like in the quadratic form. I am sure there is a better way, but thought this might help you move along until someone has a better idea.

syms f Xa Xb Za Zb Ya Yb xa=-f*Xa/Za;

xb=-f*Xb/Zb;

ya=-f*Ya/Za;

yb=-f*Yb/Zb;

D2=((xa-xb)^2+(ya-yb)^2+(Za-Zb)^2);

expand(D2)

[Walter Roberson]

collect(D2, f)

[koizomi]

thank K and Walter that help alot