How to visualize a dataset , generated in curvilinear grid, in opengl with texture maping?

I have a dataset obtained from astronomical simulation. This data was created in a curvilinear grid with polar coordinates.

The form of this dataset is a simple array (1d) of intensities, i can visualize this data in python whit the next code.

densINcgs = 8888035.76
Munit = 1.0   #solar mass
Runit = 1.0   #au
DensUnit = Munit / Runit**2.0 * densINcgs # grams / (cm^2)
# grid specification
nrad = 128 #128 #500
nsec = 384 # 256 #1500
Rmin = 0.4
Rmax = 1.8

r = np.linspace(Rmin, Rmax, nrad)
print("rx: ",np.linspace(179517444792000.0,897587223960000.2,384))

rr = []
for i in range(0,nrad):
print("lin",np.linspace(0.,2.*np.pi, nsec))
theta, rad   = np.meshgrid(np.linspace(0., 2.*np.pi, nsec), rr)
xi = rad * np.cos(theta)
yi = rad * np.sin(theta)

rho =   fromfile("dens10.dat",dtype='float32')        
Rho =          rho.reshape(nrad,nsec)

xlabel('x [AU]', fontsize=16)
ylabel('y [AU]', fontsize=16)   
cb = plt.colorbar()

cb.set_label('log Density [$\\rm g$ $\\rm cm^{-2}$]')
zc = np.linspace(0, 255, 49152).reshape(128, 384)
zc= zc.reshape(128, 384)
figure(17)How visualize a data generate in curvilinear grid in opengl




The first image is the direct visualization of the data, and the second image is ta correct visualization of the data on a curvilinear grid. I generated this visualization with pcolormesh.

But i want generate the second visualization with openGL and glsl, using texture mapping. i tried this with the next code ( a part).

Load textures

I define a quad with this vertices.

float vertices[] = {
-0.5f, -0.5f, -0.5f,  0.0f, 0.0f,
0.5f, -0.5f, -0.5f,  1.0f, 0.0f,
0.5f,  0.5f, -0.5f,  1.0f, 1.0f,
0.5f,  0.5f, -0.5f,  1.0f, 1.0f,
-0.5f,  0.5f, -0.5f,  0.0f, 1.0f,

-0.5f, -0.5f, -0.5f, 0.0f, 0.0f


i load the data set ( x=128 , y=384 )

float *pData = new   float[XDIM * YDIM];
FILE *archivo;
archivo = fopen("dens10.dat", "rb");
//  archivo=fopen("avance/media/data5.out","rb");
std::cout << "A3" << std::endl;
if (archivo != NULL){
 std::cout << "A3.1" << std::endl;
for (int i = 0; i < XDIM * YDIM ; i++)
{   //std::cout << "A3.5" << std::endl;
float v;
fread((void*)(&v), sizeof(v), 1, archivo);


and i define te textures

glGenTextures(1, &texture1);
glBindTexture(GL_TEXTURE_2D, texture1);
// set the texture wrapping parameters
// set texture filtering parameters

vertex shader

#version 330 core
layout (location = 0) in vec3 aPos;
layout (location = 1) in vec2 aTexCoord;

out vec2 TexCoord;

uniform mat4 model;
uniform mat4 view;
uniform mat4 projection;

void main()

vec4 cord = projection * view * model * vec4(aPos, 1.0f);

gl_Position = vec4(cord);


fragment shader

#version 330 core
out vec4 FragColor;

in vec2 TexCoord;

// texture samplers
uniform sampler2D texture1;
// uniform sampler2D texture2;

#define PI 3.14159265358979323844

void main()
	float c=texture(texture1,TexCoord ).r;
	// vec4 col=vec4(10000*c,30*c,20*c,1.0);
	vec4 col=vec4(c*1000,300*c,100*c,1.0);

	FragColor = col;

The result is the next.

As can be seen this image is very similar to firt image obtained in python but my intention is get a image similary to the second.

This is the dataset
[data set] (!

Thank you very much in advance.

You have two options. One is to generate a grid and transform the vertices from polar to rectangular coordinates (i.e. what pyplot.pcolormesh does). The other is to render a quad and apply the inverse transformation (rectangular to polar) to the texture coordinates. E.g.

const float pi = 3.141592653589793;
vec2 t = TexCoord*2-1; // map [0,1] -> [-1,+1]
float r = length(TexCoord); // radius
if (r > 1)
float a = atan(TexCoord.y, TexCoord.x); // angle, ccw from +X axis.
a = (a/pi+1)/2; // map [-pi,pi] => [0,1]
float c = texture(texture1,vec2(r,a)).r;

thanks for your answers.
I tried implement the inverse transformation of textures in fragment shader and i get the next image:

But this have a different form than the image get in python ( second).

About of fisrt method that you mentioned ( create a grid), casually, Do you have a example,tutorial or documentation where is explain this?.

Thanks in advance.

Change the order of the texture coordinates, i.e. vec2(a,r).

Thanks for your answers.
I changed the order of texture coordinates, and i obtained the next image.

This is very similar than second imagen, but the center is different.
How could i achieve an image with donut form? since in the python code i define that the radius have a offset of 0.4 from origin to 1.8 as max radis.

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