Peter's Projective Matlab Function

Source code

1. function circle(c, r, nsides)  % Do you use “nargin“ and “line(x,y,z)“?

2. function plotPoint(p, mark, txt)   % “text(x,y,txt)”

3. function t = homoTrans(P,v); % “t = P*v“; “ then normalized t“; x = t(1,:); y=t(2,:)

4. function hline(a,b,c) % plot 2D line from homogeneous coordinates; using “isa“

5. function c = hcross(a,b) %c = cross(a,b); c = c/c(3);

6. function [i1, i2] = circleintersect(c1, r1, c2, r2, lr)

% cosR2 = (b^2 + r1^2 - r2^2)/(2*b*r1);    sinR2 = sqrt(1-cosR2^2);

%  i1 = c1 + r1*cosR2*bv + r1*sinR2*bvp;     i2 = c1 + r1*cosR2*bv - r1*sinR2*bvp;
7. function H = homography1d(x1, x2);  %the 2x2 homography such that x2 = H*x1, using SVD

8. function H = homography2d(varargin) % like 2D counterpart, using SVD to fit into homo

%%%%%%%%%%%%%%%%%%%%%%%%%% others

• invpersp.m calculates the 3x3 homogeneous inverse transformation matrix describing the perspective transformation of a planar surface in an image. Four or more known image points are required.
• fundmatrix.m computes the fundamental matrix from 8 or more matching points in a stereo pair of images using the normalised 8 point algorithm.
• normalise2dpts.m translates and normalises a set of 2D homogeneous points so that their centroid is at the origin and their mean distance from the origin is sqrt(2). This is used to improve the conditioning of any equations used to solve homographies, fundamental matrices etc.
• hnormalise.m normalises an array of homogeneous coordinates so that their scale parameter is 1. Points at infinity are unchanged.
• imTrans.m applies a homogeneous transform to an image.
• digiplane.m allows you to digitise and transform points within a planar region in an image.
• equalAngleConstraint.m Affine transform constraints given two equal angles.
• knownAngleConstraint.m Affine transform constraints given a known angle.
• lengthRatioConstraint Affine transform constraints given a length ratio.