Transform images with bezier curves - c++

Question

I'm using this article: nonlingr as a font to understand non linear transformations, in the section GLYPHS ALONG A PATH he explains how to use a parametric curve to transform an image, i'm trying to apply a cubic bezier to an image, however i have been unsuccessfull, this is my code:
OUT.aloc(IN.width(), IN.height());
//get the control points...
wVector p0(values[vindex], values[vindex+1], 1);
wVector p1(values[vindex+2], values[vindex+3], 1);
wVector p2(values[vindex+4], values[vindex+5], 1);
wVector p3(values[vindex+6], values[vindex+7], 1);
//this is to calculate t based on x
double trange = 1 / (OUT.width()-1);
//curve coefficients
double A = (-p0[0] + 3*p1[0] - 3*p2[0] + p3[0]);
double B = (3*p0[0] - 6*p1[0] + 3*p2[0]);
double C = (-3*p0[0] + 3*p1[0]);
double D = p0[0];
double E = (-p0[1] + 3*p1[1] - 3*p2[1] + p3[1]);
double F = (3*p0[1] - 6*p1[1] + 3*p2[1]);
double G = (-3*p0[1] + 3*p1[1]);
double H = p0[1];
//apply the transformation
for(long i = 0; i < OUT.height(); i++){
for(long j = 0; j < OUT.width(); j++){
//t = x / width
double t = trange * j;
//apply the article given formulas
double x_path_d = 3*t*t*A + 2*t*B + C;
double y_path_d = 3*t*t*E + 2*t*F + G;
double angle = 3.14159265/2.0 + std::atan(y_path_d / x_path_d);
mapped_point.Set((t*t*t)*A + (t*t)*B + t*C + D + i*std::cos(angle),
(t*t*t)*E + (t*t)*F + t*G + H + i*std::sin(angle),
1);
//test if the point is inside the image
if(mapped_point[0] < 0 ||
mapped_point[0] >= OUT.width() ||
mapped_point[1] < 0 ||
mapped_point[1] >= IN.height())
continue;
OUT.setPixel(
long(mapped_point[0]),
long(mapped_point[1]),
IN.getPixel(j, i));
}
}
Applying this code in a 300x196 rgb image all i get is a black screen no matter what control points i use, is hard to find information about this kind of transformation, searching for parametric curves all i find is how to draw them, not apply to images. Can someone help me on how to transform an image with a bezier curve?

Answer 1

IMHO applying a curve to an image sound like using a LUT. So you will need to check for the value of the curve for different image values and then switch the image value with the one on the curve, so, create a Look-Up-Table for each possible value in the image (e.g : 0, 1, ..., 255, for a gray value 8 bit image), that is a 2x256 matrix, first column has the values from 0 to 255 and the second one having the value of the curve.