Geometry Geometry Math Forum

 October 8th, 2012, 07:16 AM #1 Newbie   Joined: Feb 2012 Posts: 2 Thanks: 0 Geometry: perspective projection Hello, I have a simple problem - here it is: 1) We have a camera in R3 with point of view C[0,0,-1]. 2) The projection plane of the camera is the plane z=0 (this is Ax+By+Cz+D=0 where A=B=D=0 and C=1). 3) if we want to project a point (for example G[g1,g2,g3]) to the projection plane, we construct a line through the point and C (GC). The intersection between the line (GC) and the projection plane (z=0) is the projection of our point (G'). 4) We have 3 points in space (L[l1,l2,l3], M[m1,m2,m3] and N[n1,n2,n3]), which form a triangle with width 128, height 96 and right angle at M. 5) We know the coordinates of the projections of the points L, M and N - they are L'[l1',l2',l3'], M'[m1',m2',m3'] and N'[n1',n2',n3']. We are looking for the coordinates of L, M and N. October 9th, 2012, 10:36 AM #2 Newbie   Joined: Oct 2012 Posts: 2 Thanks: 0 Re: Geometry: perspective projection I would use vectors. For a point L' in the projection plane, the actual point L = L' + a*L'' for some value of a, where L'' is any vector which is parallel to the line between C and L. Also M = M' + b*M'' and N = N' + c*N''. Plug in your constraints and solve the resulting simultaneous equations for a, b and c. You actually have a massive simplification in your case because you know that L, M and N are in the same z plane, and also the L', M' and N' are in the same z plane. This means that if you choose L'', M'' and N'' to each have a z component of 1, then a, b and c will have the same value. Tags geometry, perspective, projection Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Galux Algebra 1 September 23rd, 2012 11:25 PM Joey1987 New Users 2 July 30th, 2010 02:22 AM Tannz0rz Computer Science 1 May 16th, 2010 11:48 PM dr_jekyll Algebra 7 December 17th, 2009 01:43 PM Nicolas Calculus 0 January 7th, 2009 03:27 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      