• #### bump map from normal map ?

From Yakov Galka@21:1/5 to New Guy on Tue Sep 8 13:58:56 2015
On Sunday, April 30, 2006 at 3:26:29 AM UTC+3, New Guy wrote:
Is it possible to go backwards, and (re)create a (correct) height map from
a normal map? Is there any code already out there that does this?

Thanks.

I acknowledge that this thread is REALLY old, yet, for the sake of future googlers, here is a code that does correct reconstruction and *performs well under noise*:

#include <fftw3.h>
#include <complex>
#include <vector>

void reconstruct_height_map(const float *normal, float *dx, float *dy, int width, int height, float *result)
{
typedef std::complex<float> C;
fftwf_plan plan;

std::vector<float> nx(width*height), ny(width*height);
for(int y = 0, i = 0; y < height; ++y)
for(int x = 0; x < width; ++x, ++i, normal += 3)
nx[i] = normal[0]/normal[2], ny[i] = normal[1]/normal[2];

const int half_width = width/2 + 1;
std::vector<C> Nx(half_width*height), Ny(half_width*height);
std::vector<C> Dx(half_width*height), Dy(half_width*height);

plan = fftwf_plan_dft_r2c_2d(height, width, &nx[0], (fftwf_complex*)&Nx[0], FFTW_ESTIMATE);
fftwf_execute_dft_r2c(plan, &nx[0], (fftwf_complex*)&Nx[0]);
fftwf_execute_dft_r2c(plan, &ny[0], (fftwf_complex*)&Ny[0]);
fftwf_execute_dft_r2c(plan, &dx[0], (fftwf_complex*)&Dx[0]);
fftwf_execute_dft_r2c(plan, &dy[0], (fftwf_complex*)&Dy[0]);
fftwf_destroy_plan(plan);

std::vector<C> F(half_width*height);
for(int y = 0, i = 0; y < height; ++y)
for(int x = 0; x < half_width; ++x, ++i)
{
float denom = width * height * (norm(Dx[i]) + norm(Dy[i]));
F[i] = denom > 0 ? - (Dx[i] * Nx[i] + Dy[i] * Ny[i]) / denom : 0;
}

plan = fftwf_plan_dft_c2r_2d(height, width, (fftwf_complex*)&F[0], &result[0], FFTW_ESTIMATE);
fftwf_execute(plan);
fftwf_destroy_plan(plan);
}

void reconstruct_height_map1(const float *normal, int width, int height, float *result)
{
std::vector<float> dx(width*height), dy(width*height);
dx[0] = 1, dx[1] = -1;
dy[0] = 1, dy[width] = -1;
reconstruct_height_map(normal, &dx[0], &dy[0], width, height, result);
}

void reconstruct_height_map2(const float *normal, int width, int height, float *result)
{
std::vector<float> dx(width*height), dy(width*height);
dx[width-1] = 1, dx[1] = -1;
dy[width*(height-1)] = 1, dy[width] = -1;
reconstruct_height_map(normal, &dx[0], &dy[0], width, height, result);
}

Source (explains the math behind it): http://stannum.co.il/blog/1/reconstructing-a-height-map-from-a-normal-map

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