Three.js: How to flip normals after negative scale - three.js

I have cloned and than flipped an object using negative scale, which causes my single sided faces to inverse. My question is, how can i flip the normals too?
I don't want to use material.side = THREE.DoubleSide, for reasons: 1) didn't work properly (some shades are drawn from inside) and 2) wanna keep as much performance as possible. So DoubleSide isn't an option for me.
Thats how my object if flipped.
mesh.scale.x = - scale_width;
Thanks in advance!

I would advise against negative scale for a whole host of reasons, as explained in this link: Transforming vertex normals in three.js
You can instead apply an inversion matrix to your geometry like so
geometry.scale( - 1, 1, 1 );
As explained in the link, a consequence to doing this, however, is the geometry faces will no longer have counterclockwise winding order, but clockwise.
You can manually traverse your geometry and flip the winding order of each face. This may work for you -- if you do not have a texture applied and are not using UVs. If your geometry is to be textured, the UVs will need to be corrected, too.
Actually, a geometry inversion utility would be a nice addition to three.js. Currently, what you want to do is not supported by the library.
three.js r.72

Just dumping this here. I found somewhere flipNormals and translated it for BufferGeometry
Flip normals, flip UVs, Inverse Face winding
Version for indexed BufferGeometry
function flipBufferGeometryNormalsIndexed(geometry) {
const index = geometry.index.array
for (let i = 0, il = index.length / 3; i < il; i++) {
let x = index[i * 3]
index[i * 3] = index[i * 3 + 2]
index[i * 3 + 2] = x
}
geometry.index.needsUpdate = true
}
Version for non-indexed BufferGeometry
export function flipBufferGeometryNormals(geometry) {
const tempXYZ = [0, 0, 0];
// flip normals
for (let i = 0; i < geometry.attributes.normal.array.length / 9; i++) {
// cache a coordinates
tempXYZ[0] = geometry.attributes.normal.array[i * 9];
tempXYZ[1] = geometry.attributes.normal.array[i * 9 + 1];
tempXYZ[2] = geometry.attributes.normal.array[i * 9 + 2];
// overwrite a with c
geometry.attributes.normal.array[i * 9] =
geometry.attributes.normal.array[i * 9 + 6];
geometry.attributes.normal.array[i * 9 + 1] =
geometry.attributes.normal.array[i * 9 + 7];
geometry.attributes.normal.array[i * 9 + 2] =
geometry.attributes.normal.array[i * 9 + 8];
// overwrite c with stored a values
geometry.attributes.normal.array[i * 9 + 6] = tempXYZ[0];
geometry.attributes.normal.array[i * 9 + 7] = tempXYZ[1];
geometry.attributes.normal.array[i * 9 + 8] = tempXYZ[2];
}
// change face winding order
for (let i = 0; i < geometry.attributes.position.array.length / 9; i++) {
// cache a coordinates
tempXYZ[0] = geometry.attributes.position.array[i * 9];
tempXYZ[1] = geometry.attributes.position.array[i * 9 + 1];
tempXYZ[2] = geometry.attributes.position.array[i * 9 + 2];
// overwrite a with c
geometry.attributes.position.array[i * 9] =
geometry.attributes.position.array[i * 9 + 6];
geometry.attributes.position.array[i * 9 + 1] =
geometry.attributes.position.array[i * 9 + 7];
geometry.attributes.position.array[i * 9 + 2] =
geometry.attributes.position.array[i * 9 + 8];
// overwrite c with stored a values
geometry.attributes.position.array[i * 9 + 6] = tempXYZ[0];
geometry.attributes.position.array[i * 9 + 7] = tempXYZ[1];
geometry.attributes.position.array[i * 9 + 8] = tempXYZ[2];
}
// flip UV coordinates
for (let i = 0; i < geometry.attributes.uv.array.length / 6; i++) {
// cache a coordinates
tempXYZ[0] = geometry.attributes.uv.array[i * 6];
tempXYZ[1] = geometry.attributes.uv.array[i * 6 + 1];
// overwrite a with c
geometry.attributes.uv.array[i * 6] =
geometry.attributes.uv.array[i * 6 + 4];
geometry.attributes.uv.array[i * 6 + 1] =
geometry.attributes.uv.array[i * 6 + 5];
// overwrite c with stored a values
geometry.attributes.uv.array[i * 6 + 4] = tempXYZ[0];
geometry.attributes.uv.array[i * 6 + 5] = tempXYZ[1];
}
geometry.attributes.normal.needsUpdate = true;
geometry.attributes.position.needsUpdate = true;
geometry.attributes.uv.needsUpdate = true;
}
For old style Geometry
export function flipNormals(geometry) {
let temp = 0;
let face;
// flip every vertex normal in geometry by multiplying normal by -1
for (let i = 0; i < geometry.faces.length; i++) {
face = geometry.faces[i];
face.normal.x = -1 * face.normal.x;
face.normal.y = -1 * face.normal.y;
face.normal.z = -1 * face.normal.z;
}
// change face winding order
for (let i = 0; i < geometry.faces.length; i++) {
const face = geometry.faces[i];
temp = face.a;
face.a = face.c;
face.c = temp;
}
// flip UV coordinates
const faceVertexUvs = geometry.faceVertexUvs[0];
for (let i = 0; i < faceVertexUvs.length; i++) {
temp = faceVertexUvs[i][0];
faceVertexUvs[i][0] = faceVertexUvs[i][2];
faceVertexUvs[i][2] = temp;
}
geometry.verticesNeedUpdate = true;
geometry.normalsNeedUpdate = true;
geometry.computeFaceNormals();
geometry.computeVertexNormals();
geometry.computeBoundingSphere();
}

This question is two years old, but in case anyone passes by. Here is a non-destructive way of doing this:
You can enter the "dirty vertices/normals" mode, and flip the normals manually:
mesh.geometry.dynamic = true
mesh.geometry.__dirtyVertices = true;
mesh.geometry.__dirtyNormals = true;
mesh.flipSided = true;
//flip every vertex normal in mesh by multiplying normal by -1
for(var i = 0; i<mesh.geometry.faces.length; i++) {
mesh.geometry.faces[i].normal.x = -1*mesh.geometry.faces[i].normal.x;
mesh.geometry.faces[i].normal.y = -1*mesh.geometry.faces[i].normal.y;
mesh.geometry.faces[i].normal.z = -1*mesh.geometry.faces[i].normal.z;
}
mesh.geometry.computeVertexNormals();
mesh.geometry.computeFaceNormals();
+1 #WestLangley, I suggest you never use negative scale.

It is fixed !!
The flip of an object with a negative scale object.scale.x = -1 also reverse the normals since three.js r89 (see: Support reflection matrices. #12787).
(But I have to upgrade to r91 to solve my normal issue.)

If you have an indexed BufferGeometry it's already enough to reorder the indices like this:
let temp;
for ( let i = 0; i < geometry.index.array.length; i += 3 ) {
// swap the first and third values
temp = geometry.index.array[ i ];
geometry.index.array[ i ] = geometry.index.array[ i + 2 ];
geometry.index.array[ i + 2 ] = temp;
}

Related

How to apply white balance coefficents to RAW image for sRGB output

I want to convert RAW image data (RGGB) to sRGB image. There are many specialized ways to do this but to first understand the basics, I've implemented some easy alogrithms like debayering by resolution-reduction.
My current pipeline is:
Rescale the u16 input data by blacklevel and whitelevel
Apply white balance coefficents
Debayer with size reduction, average for G: g=((g0+g1)/2)
Calculate pseudo-inverse for D65 illuminant XYZ_TO_CAM (from Adobe DNG)
Convert debayered RGB data to XYZ by CAM_TO_XYZ
Convert XYZ to D65 sRGB (matrix taken from Bruce Lindbloom)
Apply gamma correction (simple routine for now, should be replaced by sRGB gamma)
Rescale from [minval..maxval] to [0..1] and convert f32 to u16
Save as tiff
The problem is that if I skip the white balance coefficent multiplication (or just replace them by 1.0) the output image already looks acceptable. If I apply the coefficents (taken from AsShot in DNG) the output has a huge color cast. And I'm not sure if I have to multiply by coef or 1/coef.
The first image is the result of the pipeline with wb_coefs set to 1.0.
The second image is the result with the "correct" wb_coefs.
What is wrong in my pipeline?
Additional question:
I'm not sure about the rescaling process. Do I've to rescale into [0..1] after every step or is it enough to rescale during u16 conversion as final stage?
Full code:
macro_rules! max {
($x: expr) => ($x);
($x: expr, $($z: expr),+) => {{
let y = max!($($z),*);
if $x > y {
$x
} else {
y
}
}}
}
macro_rules! min {
($x: expr) => ($x);
($x: expr, $($z: expr),+) => {{
let y = min!($($z),*);
if $x < y {
$x
} else {
y
}
}}
}
/// sRGB D65
const XYZD65_TO_SRGB: [[f32; 3]; 4] = [
[3.2404542, -1.5371385, -0.4985314],
[-0.9692660, 1.8760108, 0.0415560],
[0.0556434, -0.2040259, 1.0572252],
[0.0, 0.0, 0.0],
];
// buf: RAW image data
fn to_srgb(buf: &Vec<u16>, width: usize, height: usize) {
let w = width / 2;
let h = height / 2;
let blacklevel: [u16; 4] = [511, 511, 511, 511];
let whitelevel: [u16; 4] = [12735, 12735, 12735, 12735];
let xyz2cam_d65: [[i32; 3]; 4] = [[6722, -635, -963], [-4287, 12460, 2028], [-908, 2162, 5668], [0, 0, 0]];
let cam2xyz = convert_matrix::<4>(xyz2cam_d65);
eprintln!("CAM_TO_XYZ: {:?}", cam2xyz);
// from DNG
// As Shot Neutral: 0.518481 1 0.545842
//let wb_coef = [1.0/0.518481, 1.0, 1.0, 1.0/0.545842];
//let wb_coef = [0.518481, 1.0, 1.0, 0.545842];
let wb_coef = [1.0, 1.0, 1.0, 1.0];
// b/w level correction, rescale, debayer
let mut rgb = vec![0.0_f32; width / 2 * height / 2 * 3];
for row in 0..h {
for col in 0..w {
let r0 = buf[(row * 2 + 0) * width + (col * 2) + 0];
let g0 = buf[(row * 2 + 0) * width + (col * 2) + 1];
let g1 = buf[(row * 2 + 1) * width + (col * 2) + 0];
let b0 = buf[(row * 2 + 1) * width + (col * 2) + 1];
let r0 = ((r0.saturating_sub(blacklevel[0])) as f32 / (whitelevel[0] - blacklevel[0]) as f32) * wb_coef[0];
let g0 = ((g0.saturating_sub(blacklevel[1])) as f32 / (whitelevel[1] - blacklevel[1]) as f32) * wb_coef[1];
let g1 = ((g1.saturating_sub(blacklevel[2])) as f32 / (whitelevel[2] - blacklevel[2]) as f32) * wb_coef[2];
let b0 = ((b0.saturating_sub(blacklevel[3])) as f32 / (whitelevel[3] - blacklevel[3]) as f32) * wb_coef[3];
rgb[row * w * 3 + (col * 3) + 0] = r0;
rgb[row * w * 3 + (col * 3) + 1] = (g0 + g1) / 2.0;
rgb[row * w * 3 + (col * 3) + 2] = b0;
}
}
// Convert to XYZ by CAM_TO_XYZ from D65 illuminant
let mut xyz = vec![0.0_f32; w * h * 3];
for row in 0..h {
for col in 0..w {
let r = rgb[row * w * 3 + (col * 3) + 0];
let g = rgb[row * w * 3 + (col * 3) + 1];
let b = rgb[row * w * 3 + (col * 3) + 2];
xyz[row * w * 3 + (col * 3) + 0] = cam2xyz[0][0] * r + cam2xyz[0][1] * g + cam2xyz[0][2] * b;
xyz[row * w * 3 + (col * 3) + 1] = cam2xyz[1][0] * r + cam2xyz[1][1] * g + cam2xyz[1][2] * b;
xyz[row * w * 3 + (col * 3) + 2] = cam2xyz[2][0] * r + cam2xyz[2][1] * g + cam2xyz[2][2] * b;
}
}
// Track min/max value for rescaling/clipping
let mut maxval = 1.0;
let mut minval = 0.0;
// Convert to sRGB from XYZ
let mut srgb = vec![0.0; w * h * 3];
for row in 0..h {
for col in 0..w {
let r = xyz[row * w * 3 + (col * 3) + 0] as f32;
let g = xyz[row * w * 3 + (col * 3) + 1] as f32;
let b = xyz[row * w * 3 + (col * 3) + 2] as f32;
srgb[row * w * 3 + (col * 3) + 0] = XYZD65_TO_SRGB[0][0] * r + XYZD65_TO_SRGB[0][1] * g + XYZD65_TO_SRGB[0][2] * b;
srgb[row * w * 3 + (col * 3) + 1] = XYZD65_TO_SRGB[1][0] * r + XYZD65_TO_SRGB[1][1] * g + XYZD65_TO_SRGB[1][2] * b;
srgb[row * w * 3 + (col * 3) + 2] = XYZD65_TO_SRGB[2][0] * r + XYZD65_TO_SRGB[2][1] * g + XYZD65_TO_SRGB[2][2] * b;
let r = srgb[row * w * 3 + (col * 3) + 0];
let g = srgb[row * w * 3 + (col * 3) + 1];
let b = srgb[row * w * 3 + (col * 3) + 2];
maxval = max!(maxval, r, g, b);
minval = min!(minval, r, g, b);
}
}
gamma_corr(&mut srgb, w, h, 2.2);
let mut output = vec![0_u16; w * h * 3];
for row in 0..h {
for col in 0..w {
let r = srgb[row * w * 3 + (col * 3) + 0];
let g = srgb[row * w * 3 + (col * 3) + 1];
let b = srgb[row * w * 3 + (col * 3) + 2];
output[row * w * 3 + (col * 3) + 0] = (clip(r, minval, maxval) * (u16::MAX as f32)) as u16;
output[row * w * 3 + (col * 3) + 1] = (clip(g, minval, maxval) * (u16::MAX as f32)) as u16;
output[row * w * 3 + (col * 3) + 2] = (clip(b, minval, maxval) * (u16::MAX as f32)) as u16;
}
}
let img = DynamicImage::ImageRgb16(ImageBuffer::from_raw(w as u32, h as u32, output).unwrap());
img.save_with_format("/tmp/test.tif", image::ImageFormat::Tiff).unwrap();
}
fn pseudoinverse<const N: usize>(matrix: [[f32; 3]; N]) -> [[f32; 3]; N] {
let mut result: [[f32; 3]; N] = [Default::default(); N];
let mut work: [[f32; 6]; 3] = [Default::default(); 3];
let mut num: f32 = 0.0;
for i in 0..3 {
for j in 0..6 {
work[i][j] = if j == i + 3 { 1.0 } else { 0.0 };
}
for j in 0..3 {
for k in 0..N {
work[i][j] += matrix[k][i] * matrix[k][j];
}
}
}
for i in 0..3 {
num = work[i][i];
for j in 0..6 {
work[i][j] /= num;
}
for k in 0..3 {
if k == i {
continue;
}
num = work[k][i];
for j in 0..6 {
work[k][j] -= work[i][j] * num;
}
}
}
for i in 0..N {
for j in 0..3 {
result[i][j] = 0.0;
for k in 0..3 {
result[i][j] += work[j][k + 3] * matrix[i][k];
}
}
}
result
}
fn convert_matrix<const N: usize>(adobe_xyz_to_cam: [[i32; 3]; N]) -> [[f32; N]; 3] {
let mut xyz_to_cam: [[f32; 3]; N] = [[0.0; 3]; N];
let mut cam_to_xyz: [[f32; N]; 3] = [[0.0; N]; 3];
for i in 0..N {
for j in 0..3 {
xyz_to_cam[i][j] = adobe_xyz_to_cam[i][j] as f32 / 10000.0;
}
}
eprintln!("XYZ_TO_CAM: {:?}", xyz_to_cam);
let inverse = pseudoinverse::<N>(xyz_to_cam);
for i in 0..3 {
for j in 0..N {
cam_to_xyz[i][j] = inverse[j][i];
}
}
cam_to_xyz
}
fn clip(v: f32, minval: f32, maxval: f32) -> f32 {
(v + minval.abs()) / (maxval + minval.abs())
}
// https://kosinix.github.io/raster/docs/src/raster/filter.rs.html#339-359
fn gamma_corr(rgb: &mut Vec<f32>, w: usize, h: usize, gamma: f32) {
for row in 0..h {
for col in 0..w {
let r = rgb[row * w * 3 + (col * 3) + 0];
let g = rgb[row * w * 3 + (col * 3) + 1];
let b = rgb[row * w * 3 + (col * 3) + 2];
rgb[row * w * 3 + (col * 3) + 0] = r.powf(1.0 / gamma);
rgb[row * w * 3 + (col * 3) + 1] = g.powf(1.0 / gamma);
rgb[row * w * 3 + (col * 3) + 2] = b.powf(1.0 / gamma);
}
}
}
The DNG for this example can be found at: https://chaospixel.com/pub/misc/dng/sample.dng (~40 MiB).
The main reason for getting wrong colors is that we have to normalize the rows of rgb2cam matrix to 1, as described in the following guide.
According to DNG spec:
ColorMatrix1 defines a transformation matrix that converts XYZ values to reference camera native color space values, under the first calibration illuminant.
It means that if the calibration illuminant is D65, the ColorMatrix converts XYZ to "camera RGB".
(Convert it as is, without using any white balance scaling coefficients).
The inverse ColorMatrix, converts from "camera RGB" to XYZ.
After converting XYZ to sRGB, the result is color balanced sRGB.
The conclusions is that ColorMatrix includes the while balance coefficients in it (the white balancing coefficients apply D65 illuminant).
Normalizing the rows of rgb2cam to 1 neutralizes the while balance coefficients, and keeps only the "Color Correction Matrix" (the math is a bit complicated).
Without normalizing the rows, we are scaling by while balance multipliers two times:
Scale coefficients from ColorMatrix that balances the input to D65.
Scale coefficients taken from AsShotNatural that balances the input to the illuminant of the scene (illuminant of the scene is close to D65).
The result of scaling twice is an extreme color cast.
Tracking the maximum in order to avoid "magenta cast in the highlights":
Instead of tracking the actual maximum color values in the input image, we suppose to track the "theoretical maximum color value".
Take whitelevel - blacklevel and scale by the white balance multipliers.
Track the result...
The guiding rule is that the colors supposed to be the same in both cases:
Applying the processing to small patches of the image, and places the patches together (where we can't track the global minimum and maximum).
Applying the processing to the entire image.
I suppose you have to track the maximum of scaled whitelevel - blacklevel, only when white balance multipliers are less than 1.
When all the multipliers are 1 or above, we can clip the result to 1.0, without tracking the maximum.
Note:
there is probably an advantage of scaling down, and tracking the maximum, but I don't know this subject.
In my solution we just multiply upper (above 1.0), and clip the result.
The solution is based on Processing RAW Images in MATLAB guide.
I am posting both MATLAB implementation and Python implementation (but no Rust implementation).
The first step is extracting the raw Bayer image from sample.dng using dcraw command line:
dcraw -4 -D -T sample.dng
Rename the tiff output to sample__lin_bayer.tif.
Conversion process:
Rescale the uint16 input data by blacklevel and whitelevel (subtract blacklevel from all the pixels and scale by whitelevel - blacklevel).
Apply white balance scaling coefficients.
The scaling coefficients equals 1./AsShotNatural.
Scale the red pixels in the Bayer alignment by the red scaling coefficient, scale the greens by the green scaling, and the blues by the blue scaling.
Assumption: the minimum scaling is 1.0 and the others are above 1.0 (we my divide by the minimum scaling to make sure).
Clip the scaled result to [0, 1] (clipping is required due to demosaic implementation limitations).
Demosaicing (Debayer) using MATLAB demosaic function or cv2.cvtColor in Python.
Calculate rgb2cam matrix: rgb2cam = ColorMatrix * rgb2xyz.
rgb2xyz matrix is taken from Bruce Lindbloom site.
Normalize rows of rgb2cam matrix so the sum of each row equals 1 (divide each row by the sum of the row).
Compute cam2rgb matrix by inverting rgb2cam: cam2rgb = inv(rgb2cam).
cam2rgb is the "CCM matrix" (Color Correction Matrix).
Left multiply matrix cam2rgb by each RGB tuple (apply color correction).
Apply gamma correction (use sRGB standard gamma).
Convert to uint8 and save as PNG (PNG format is used for posting in SO website).
MATLAB Implementation:
filename = 'sample__lin_bayer.tif'; % Output of: dcraw -4 -D -T sample.dng
% Exif information:
blacklevel = 511; % blacklevel = meta_info.SubIFDs{1}.BlackLevel(1);
whitelevel = 12735; % whitelevel = meta_info.SubIFDs{1}.WhiteLevel;
AsShotNeutral = [0.5185 1 0.5458];
ColorMatrix = [ 0.6722 -0.0635 -0.0963
-0.4287 1.2460 0.2028
-0.0908 0.2162 0.5668];
bayer_type = 'rggb';
% Constant matrix for converting sRGB to XYZ(D65):
% http://www.brucelindbloom.com/Eqn_RGB_XYZ_Matrix.html
rgb2xyz = [0.4124564 0.3575761 0.1804375
0.2126729 0.7151522 0.0721750
0.0193339 0.1191920 0.9503041];
% Read input image (Bayer mosaic alignment, pixels data type is uint16):
raw = imread(filename);
% "Linearizing":
% There is no LinearizationTable so we only have to subtract the black level.
% Convert from range [blacklevel, whitelevel] to range [0, 1].
lin_bayer = (double(raw) - blacklevel) / (whitelevel - blacklevel);
lin_bayer = max(0, min(lin_bayer, 1));
% The White Balance multipliers are 1./AsShotNeutral
wb_multipliers = 1./AsShotNeutral;
r_scale = wb_multipliers(1); % Assume value is above 1
g_scale = wb_multipliers(2); % Assume value = 1
b_scale = wb_multipliers(3); % Assume value is above 1
% Bayer alignment is RGGB:
% R G
% G B
%
% Apply white balancing to linear Bayer image.
balanced_bayer = lin_bayer;
balanced_bayer(1:2:end, 1:2:end) = balanced_bayer(1:2:end, 1:2:end)*r_scale; % Red (indices [1, 3, 5,... ; 1, 3, 5,... ])
balanced_bayer(1:2:end, 2:2:end) = balanced_bayer(1:2:end, 2:2:end)*g_scale; % Green (indices [1, 3, 5,... ; 2, 4, 6,... ])
balanced_bayer(2:2:end, 1:2:end) = balanced_bayer(2:2:end, 1:2:end)*g_scale; % Green (indices [2, 4, 6,... ; 1, 3, 5,... ])
balanced_bayer(2:2:end, 2:2:end) = balanced_bayer(2:2:end, 2:2:end)*b_scale; % Blue (indices [2, 4, 6,... ; 2, 4, 6,... ])
% Clip to range [0, 1] for avoiding "pinkish highlights" (avoiding "magenta cast" in the highlights).
balanced_bayer = min(balanced_bayer, 1);
% Demosaicing
temp = uint16(balanced_bayer*(2^16-1)); % Convert from double to uint16, because MATLAB demosaic() function requires a uint8 or uint16 input.
lin_rgb = double(demosaic(temp, bayer_type))/(2^16-1); % Apply Demosaicing and convert range back type double and range [0, 1].
% Color Space Conversion
xyz2cam = ColorMatrix; % ColorMatrix applies XYZ(D65) to CAM_rgb
rgb2cam = xyz2cam * rgb2xyz;
% Result:
% rgb2cam = [0.2619 0.1835 0.0252
% 0.0921 0.7620 0.2053
% 0.0195 0.1897 0.5379]
% Normalize rows to 1. MATLAB shortcut: rgb2cam = rgb2cam ./ repmat(sum(rgb2cam,2),1,3);
rows_sum = sum(rgb2cam, 2);
% Result:
% rows_sum = [0.4706
% 1.0593
% 0.7470]
% Divide element of every row by the sum of the row:
rgb2cam(1, :) = rgb2cam(1, :) / rows_sum(1); % Divide top row
rgb2cam(2, :) = rgb2cam(2, :) / rows_sum(2); % Divide center row
rgb2cam(3, :) = rgb2cam(3, :) / rows_sum(3); % Divide bottom row
% Result (sum of every row is 1):
% rgb2cam = [0.5566 0.3899 0.0535
% 0.0869 0.7193 0.1938
% 0.0261 0.2539 0.7200]
cam2rgb = inv(rgb2cam); % Invert matrix
% Result:
% cam2rgb = [ 1.9644 -1.1197 0.1553
% -0.2412 1.6738 -0.4326
% 0.0139 -0.5498 1.5359]
R = lin_rgb(:, :, 1);
G = lin_rgb(:, :, 2);
B = lin_rgb(:, :, 3);
% Left multiply matrix cam2rgb by each RGB tuple (convert from "camera RGB" to "linear sRGB").
sR = cam2rgb(1,1)*R + cam2rgb(1,2)*G + cam2rgb(1,3)*B;
sG = cam2rgb(2,1)*R + cam2rgb(2,2)*G + cam2rgb(2,3)*B;
sB = cam2rgb(3,1)*R + cam2rgb(3,2)*G + cam2rgb(3,3)*B;
lin_srgb = cat(3, sR, sG, sB);
lin_srgb = max(min(lin_srgb, 1), 0); % Clip to range [0, 1]
% Convet from "Linear sRGB" to sRGB (apply gamma)
sRGB = lin2rgb(lin_srgb); % lin2rgb MATLAB functions uses the exact formula [you may approximate it to power of (1/gamma)].
% Show the result, and save to sRGB.png
figure;imshow(sRGB);impixelinfo;title('sRGB');
imwrite(im2uint8(sRGB), 'sRGB.png');
% Inverting 3x3 matrix (some help of MATLAB Symbolic Toolbox):
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Assume:
% A = [ a11, a12, a13]
% [ a21, a22, a23]
% [ a31, a32, a33]
%
% 1. Compute determinant of A:
% detA = a11*a22*a33 - a11*a23*a32 - a12*a21*a33 + a12*a23*a31 + a13*a21*a32 - a13*a22*a31
%
% 2. Compute the inverse of the matrix A:
% invA = [ (a22*a33 - a23*a32)/detA, -(a12*a33 - a13*a32)/detA, (a12*a23 - a13*a22)/detA
% -(a21*a33 - a23*a31)/detA, (a11*a33 - a13*a31)/detA, -(a11*a23 - a13*a21)/detA
% (a21*a32 - a22*a31)/detA, -(a11*a32 - a12*a31)/detA, (a11*a22 - a12*a21)/detA]
Python implementation:
import numpy as np
import cv2
def lin2rgb(im):
""" Convert im from "Linear sRGB" to sRGB - apply Gamma. """
# sRGB standard applies gamma = 2.4, Break Point = 0.00304 (and computed Slope = 12.92)
g = 2.4
bp = 0.00304
inv_g = 1/g
sls = 1 / (g/(bp**(inv_g - 1)) - g*bp + bp)
fs = g*sls / (bp**(inv_g - 1))
co = fs*bp**(inv_g) - sls*bp
srgb = im.copy()
srgb[im <= bp] = sls * im[im <= bp]
srgb[im > bp] = np.power(fs*im[im > bp], inv_g) - co
return srgb
filename = 'sample__lin_bayer.tif' # Output of: dcraw -4 -D -T sample.dng
# Exif information:
blacklevel = 511
whitelevel = 12735
AsShotNeutral = np.array([0.5185, 1, 0.5458])
ColorMatrix = np.array([[ 0.6722, -0.0635, -0.0963],
[-0.4287, 1.2460, 0.2028],
[-0.0908, 0.2162, 0.5668]])
# bayer_type = 'rggb'
# Constant matrix for converting sRGB to XYZ(D65):
# http://www.brucelindbloom.com/Eqn_RGB_XYZ_Matrix.html
rgb2xyz = np.array([[0.4124564, 0.3575761, 0.1804375],
[0.2126729, 0.7151522, 0.0721750],
[0.0193339, 0.1191920, 0.9503041]])
# Read input image (Bayer mosaic alignement, pixeles data type is np.uint16):
raw = cv2.imread(filename, cv2.IMREAD_UNCHANGED)
# "Linearizing":
# There is no LinearizationTable so we only have to subtract the black level.
# Convert from range [blacklevel, whitelevel] to range [0, 1] (convert type to np.float64).
lin_bayer = (raw.astype(np.float64) - blacklevel) / (whitelevel - blacklevel)
lin_bayer = lin_bayer.clip(0, 1)
# The White Balance multipliers are 1./AsShotNeutral
wb_multipliers = 1 / AsShotNeutral
r_scale = wb_multipliers[0] # Assume value is above 1
g_scale = wb_multipliers[1] # Assume value = 1
b_scale = wb_multipliers[2] # Assume value is above 1
# Bayer alignment is RGGB:
# R G
# G B
#
# Apply white balancing to linear Bayer image.
balanced_bayer = lin_bayer.copy()
balanced_bayer[0::2, 0::2] = balanced_bayer[0::2, 0::2]*r_scale # Red (indices [0, 2, 4,... ; 0, 2, 4,... ])
balanced_bayer[0::2, 1::2] = balanced_bayer[0::2, 1::2]*g_scale # Green (indices [0, 2, 4,... ; 1, 3, 5,... ])
balanced_bayer[1::2, 0::2] = balanced_bayer[1::2, 0::2]*g_scale # Green (indices [1, 3, 5,... ; 0, 2, 4,... ])
balanced_bayer[1::2, 1::2] = balanced_bayer[1::2, 1::2]*b_scale # Blue (indices [1, 3, 5,... ; 0, 2, 4,... ])
# Clip to range [0, 1] for avoiding "pinkish highlights" (avoiding "magenta cast" in the highlights).
balanced_bayer = np.minimum(balanced_bayer, 1)
# Demosaicing:
temp = np.round((balanced_bayer*(2**16-1))).astype(np.uint16) # Convert from double to np.uint16, because OpenCV demosaic() function requires a uint8 or uint16 input.
lin_rgb = cv2.cvtColor(temp, cv2.COLOR_BayerBG2RGB).astype(np.float64)/(2**16-1) # Apply Demosaicing and convert back to np.float64 in range [0, 1] (is there a bug in OpenCV Bayer naming?).
# Color Space Conversion
xyz2cam = ColorMatrix # ColorMatrix applies XYZ(D65) to CAM_rgb
rgb2cam = xyz2cam # rgb2xyz
# Result:
# rgb2cam = [0.2619 0.1835 0.0252
# 0.0921 0.7620 0.2053
# 0.0195 0.1897 0.5379]
# Normalize rows to 1. MATLAB shortcut: rgb2cam = rgb2cam ./ repmat(sum(rgb2cam,2),1,3);
rows_sum = np.sum(rgb2cam, 1)
# Result:
# rows_sum = [0.4706
# 1.0593
# 0.7470]
# Divide element of every row by the sum of the row:
rgb2cam[0, :] = rgb2cam[0, :] / rows_sum[0] # Divide top row
rgb2cam[1, :] = rgb2cam[1, :] / rows_sum[1] # Divide center row
rgb2cam[2, :] = rgb2cam[2, :] / rows_sum[2] # Divide bottom row
# Result (sum of every row is 1):
# rgb2cam = [0.5566 0.3899 0.0535
# 0.0869 0.7193 0.1938
# 0.0261 0.2539 0.7200]
cam2rgb = np.linalg.inv(rgb2cam) # Invert matrix
# Result:
# cam2rgb = [ 1.9644 -1.1197 0.1553
# -0.2412 1.6738 -0.4326
# 0.0139 -0.5498 1.5359]
r = lin_rgb[:, :, 0]
g = lin_rgb[:, :, 1]
b = lin_rgb[:, :, 2]
# Left multiply matrix cam2rgb by each RGB tuple (convert from "camera RGB" to "linear sRGB").
sr = cam2rgb[0, 0]*r + cam2rgb[0, 1]*g + cam2rgb[0, 2]*b
sg = cam2rgb[1, 0]*r + cam2rgb[1, 1]*g + cam2rgb[1, 2]*b
sb = cam2rgb[2, 0]*r + cam2rgb[2, 1]*g + cam2rgb[2, 2]*b
lin_srgb = np.dstack([sr, sg, sb])
lin_srgb = lin_srgb.clip(0, 1) # Clip to range [0, 1]
# Convert from "Linear sRGB" to sRGB (apply gamma)
sRGB = lin2rgb(lin_srgb) # lin2rgb MATLAB functions uses the exact formula [you may approximate it to power of (1/gamma)].
# Save to sRGB.png
cv2.imwrite('sRGB.png', cv2.cvtColor((sRGB*255).astype(np.uint8), cv2.COLOR_RGB2BGR))
Results (downscaled):
Result of RawTherapee (all enhancements are disabled):
MATLAB result:
Python result:
Note:
The result looks dark due to low exposure (and because we didn't apply any brightness correction).

How to properly process images with mixed noise types

The picture with noise is like this.
Noised picture: Image3.bmp
I was doing image processing in MatLab with some built-in and self-implemented filters.
I have already tried a combination of bilateral, median and gaussian. bilateral and gaussian code are at the end of this post.
img3 = double(imread('Image3.bmp')); % this is the noised image
lena = double(imread('lena_gray.jpg')); % this is the original one
img3_com = bilateral(img3, 3, 2, 80);
img3_com = medfilt2(img3_com, [3 3], 'symmetric');
img3_com = gaussian(img3_com, 3, 0.5);
img3_com = bilateral(double(img3_com), 6, 100, 13);
SNR3_com = snr(img3_com,img3_com - lena); % 17.1107
However, the result is not promising with SNR of only 17.11.
Filtered image: img3_com
The original picture is like this.
Clean original image: lena_gray.jpg
Could you please give me any possible ideas about how to process it? Like what noise generators generated the noised image and what filtering methods or image processing method I can use to deal with it. Appreciate!!!
My bilateral function bilateral.m
function img_new = bilateral(img_gray, window, sigmaS, sigmaI)
imgSize = size(img_gray);
img_new = zeros(imgSize);
for i = 1:imgSize(1)
for j = 1:imgSize(2)
sum = 0;
simiSum = 0;
for a = -window:window
for b = -window:window
x = i + a;
y = j + b;
p = img_gray(i,j);
q = 0;
if x < 1 || y < 1 || x > imgSize(1) || y > imgSize(2)
% q=0;
continue;
else
q = img_gray(x,y);
end
gaussianFilter = exp( - double((a)^2 + (b)^2)/ (2 * sigmaS^2 ) - (double(p-q)^2)/ (2 * sigmaI^2 ));
% gaussianFilter = gaussian((a^2 + b^2)^(1/2), sigma) * gaussian(abs(p-q), sigma);
sum = sum + gaussianFilter * q;
simiSum = simiSum + gaussianFilter;
end
end
img_new(i,j) = sum/simiSum;
end
end
% disp SNR
lena = double(imread('lena_gray.jpg'));
SNR1_4_ = snr(img_new,img_new - lena);
disp(SNR1_4_);
My gaussian implementation gaussian.m
function img_gau = gaussian(img, hsize, sigma)
h = fspecial('gaussian', hsize, sigma);
img_gau = conv2(img,h,'same');
% disp SNR
lena = double(imread('lena_gray.jpg'));
SNR1_4_ = snr(img_gau,img_gau - lena);
disp(SNR1_4_);

How to calculate the mean of 3D matrices in an image without NaN?

I need to calculate the mean of a 3D matrices (last step in the code). However, there are many NaNs in the (diff_dataframe./dataframe_vor) calculation. So when I use this code, some results will be NaN. How could I calculate the mean of this matrix by ignoring the NaNs? I attached the code as below.
S.amplitude = 1:20;%:20;
S.blocksize = [1 2 3 4 5 6 8 10 12 15 20];
S.frameWidth = 1920;
S.frameHeight = 1080;
S.quality=0:10:100;
image = 127*ones(S.frameHeight,S.frameWidth,3);
S.yuv2rgb = [1 0 1.28033; 1 -0.21482 -0.38059; 1 2.12798 0];
i_bs = 0;
for BS = S.blocksize
i_bs = i_bs + 1;
hblocks = S.frameWidth / BS;
vblocks = S.frameHeight / BS;
i_a = 0;
dataU = randi([0 1],vblocks,hblocks);
dataV = randi([0 1],vblocks,hblocks);
dataframe_yuv = zeros(S.frameHeight, S.frameWidth, 3);
for x = 1 : hblocks
for y = 1 : vblocks
dataframe_yuv((y-1)*BS+1:y*BS, ...
(x-1)*BS+1:x*BS, 2) = dataU(y,x) * 2 - 1;
dataframe_yuv((y-1)*BS+1:y*BS, ...
(x-1)*BS+1:x*BS, 3) = dataV(y,x) * 2 - 1;
end
end
dataframe_rgb(:,:,1) = S.yuv2rgb(1,1) * dataframe_yuv(:,:,1) + ...
S.yuv2rgb(1,2) * dataframe_yuv(:,:,2) + ...
S.yuv2rgb(1,3) * dataframe_yuv(:,:,3);
dataframe_rgb(:,:,2) = S.yuv2rgb(2,1) * dataframe_yuv(:,:,1) + ...
S.yuv2rgb(2,2) * dataframe_yuv(:,:,2) + ...
S.yuv2rgb(2,3) * dataframe_yuv(:,:,3);
dataframe_rgb(:,:,3) = S.yuv2rgb(3,1) * dataframe_yuv(:,:,1) + ...
S.yuv2rgb(3,2) * dataframe_yuv(:,:,2) + ...
S.yuv2rgb(3,3) * dataframe_yuv(:,:,3);
for A = S.amplitude
i_a = i_a + 1;
i_q = 0;
image1p = round(image + dataframe_rgb * A);
image1n = round(image - dataframe_rgb * A);
dataframe_vor = ((image1p-image1n)/2)/255;
for Q = S.quality
i_q = i_q + 1;
namestrp = ['greyjpegs/Img_BS' num2str(BS) '_A' num2str(A) '_Q' num2str(Q) '_1p.jpg'];
namestrn = ['greyjpegs/Img_BS' num2str(BS) '_A' num2str(A) '_Q' num2str(Q) '_1n.jpg'];
imwrite(image1p/255,namestrp,'jpg', 'Quality', Q);
imwrite(image1n/255,namestrn,'jpg', 'Quality', Q);
error_mean(i_bs, i_a, i_q) = mean2((abs(diff_dataframe./dataframe_vor)));
end
end
end
mean2 is a shortcut function that's part of the image processing toolbox that finds the entire average of a 2D region which doesn't include handling NaN. In that case, simply remove all values that are NaN and find the resulting average. Note that the removal of NaN unrolls the 2D region into a 1D vector, so we can simply use mean in this case. As an additional check, let's make sure there are no divide by 0 errors, so also check for Inf as well.
Therefore, replace this line:
error_mean(i_bs, i_a, i_q) = mean2((abs(diff_dataframe./dataframe_vor)));
... with:
tmp = abs(diff_dataframe ./ dataframe_vor);
mask = ~isnan(tmp) | ~isinf(tmp);
tmp = tmp(mask);
if isempty(tmp)
error_mean(i_bs, i_a, i_q) = 0;
else
error_mean(i_bs, i_a, i_q) = mean(tmp);
We first assign the desired operation to a temporary variable, use isnan and isinf to remove out the offending values, then find the average of the rest. One intricacy is that if your entire region is NaN or Inf, then the removal of all these entries in the region results in the empty vector, and finding the mean of this undefined. A separate check is there to be sure that if it's empty, simply assign the value of 0 instead.

Particle system running slowly

here is update function. As soon as i turn update on my program gets slower. I'm not even able to render 25000 particles at a time. Voxels is a 3 dimensional array. How to i change my update function so that the calculations is done faster. i want to able to render at least 100000 particles.
function update(){
newTime = Date.now();
elapsedTime = newTime - oldTime;
oldTime = newTime;
for(var index =0 ; index < particles.vertices.length; index++){
//particle's old position
var oldPosition = particles.vertices[index];
//making sure particles do not og out of boundary
if (oldPosition.x > screenSquareLength || oldPosition.x < -screenSquareLength){
oldPosition.x = 2 * screenSquareLength * Math.random() - screenSquareLength;
}
if (oldPosition.y > screenSquareLength || oldPosition.y < -screenSquareLength){
oldPosition.y = 2 * screenSquareLength * Math.random() - screenSquareLength;
}
if (oldPosition.z > screenSquareDepth/2 || oldPosition.z < -screenSquareDepth/2){
oldPosition.z = screenSquareDepth * Math.random() - screenSquareDepth/2;
}
var oldVelocity = particlesExtraInfo[index].velocity;
var fieldVelocity;
var xIndex, yIndex, zIndex;
try{
//calculating index of voxel
xIndex = Math.floor(( oldPosition.x + screenSquareLength ) / voxelSize);
yIndex = Math.floor(( oldPosition.y + screenSquareLength ) / voxelSize);
zIndex = Math.floor(( screenSquareDepth / 2 - oldPosition.z) / voxelSize);
//getting velocity, color for particle and if voxel is
fieldVelocity = voxels[zIndex][xIndex][yIndex].userData["velocity"];
particleColor = voxels[zIndex][xIndex][yIndex].userData["color"];
activeVoxel = voxels[zIndex][xIndex][yIndex].userData["visible"];
}catch (e){
console.log("indexX = "+xIndex + " \t Yindex = "+ yIndex+" \t zIndex = "+ zIndex);
}
var particleColor;
var activeVoxel;
try{
var vx = ((oldVelocity.x + fieldVelocity.x) * elapsedTime);
var vy = ((oldVelocity.y + fieldVelocity.y) * elapsedTime);
var vz = ((oldVelocity.z + fieldVelocity.z) * elapsedTime);
var magnitude = Math.abs(vx) + Math.abs(vy) + Math.abs(vz); //Math.sqrt(vx*vx + vy*vy+ vz*vz);
var normalized = new THREE.Vector3(vx / magnitude, vy / magnitude, vz / magnitude);
if((particles.vertices[index].x < 0.1 && particles.vertices[index].x > -0.1) && (particles.vertices[index].y < 0.1 && particles.vertices[index].y > -0.1) && (particles.vertices[index].z < 0.1 && particles.vertices[index].z > -0.1) ){
particles.vertices[index].x = 2 * screenSquareLength * Math.random() - screenSquareLength;;
particles.vertices[index].y = 2 * screenSquareLength * Math.random() - screenSquareLength;;
particles.vertices[index].z = 2 * screenSquareLength * Math.random() - screenSquareLength;;
}
//if voxel is not part of the model update particle postion and velocity
if( activeVoxel == 0){
particles.colors[index] = new THREE.Color(particleColor);//new THREE.Color(0, 0, 1);
particles.colorsNeedUpdate = true;
particles.vertices[index].x += normalized.x/slowingFactor;
particles.vertices[index].y += normalized.y/slowingFactor;
particles.vertices[index].z += normalized.z/slowingFactor;
particles.verticesNeedUpdate = true;
particlesExtraInfo[index].velocity = normalized;
}else{
//voxel is part of particle so update color property of particle
particles.colors[index] = new THREE.Color(0, 0, 1);
particles.colorsNeedUpdate = true;
particles.vertices[index].x += normalized.x/(slowingFactor * 200);
particles.vertices[index].y += normalized.y/(slowingFactor * 200);
particles.vertices[index].z += normalized.z/(slowingFactor * 200);
particles.verticesNeedUpdate = true;
particlesExtraInfo[index].velocity = new THREE.Vector3( normalized.x/slowingFactor, normalized.y/slowingFactor, normalized.z/slowingFactor );
}
}catch(e){
}
}
}
I don't know much about what exactly happens when you update a buffer like this, but I know that it can be slow.
While 25k may be a lot for what you're trying to do (i experimented with 5k and had trouble) there is no reason why you can't optimize your JS before trying to move everything to the gpu (for example).
var foo = 0;
foo+= normalized.x / someFactor;
//better done this way:
var invSomeFactor = 1/someFactor;
// now you avoid dividing the same thing many times in your loop
foo += normalized.x * invSomeFactor;
Math.random() is pretty expensive, you could make a look up table (a large one) and fetch these precomputed values from it.
var myLookupTable = [];
var MAX_VALUES = 2048;
for ( var i = 0 ; i < MAX_VALUES ; i ++ ){
myLookupTable.push(Math.random());
}
//and then you can have a stride for example
var RAND_STRIDE = 0;
//and in the loop
someVec.x += something.x * myLookupTable[ RAND_STRIDE ++ ];
RAND_STRIDE %= MAX_VALUES; //read from the beginning
Finally, you can write a fragment shader, that would read from a buffer, and write into another buffer doing all this logic in the process. Each fragment is your particle and once you run this pass and compute your positions, you need to be able to read the buffer in your particle vertex shader and just assign those positions.

Choosing an attractive linear scale for a graph's Y Axis

I'm writing a bit of code to display a bar (or line) graph in our software. Everything's going fine. The thing that's got me stumped is labeling the Y axis.
The caller can tell me how finely they want the Y scale labeled, but I seem to be stuck on exactly what to label them in an "attractive" kind of way. I can't describe "attractive", and probably neither can you, but we know it when we see it, right?
So if the data points are:
15, 234, 140, 65, 90
And the user asks for 10 labels on the Y axis, a little bit of finagling with paper and pencil comes up with:
0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250
So there's 10 there (not including 0), the last one extends just beyond the highest value (234 < 250), and it's a "nice" increment of 25 each. If they asked for 8 labels, an increment of 30 would have looked nice:
0, 30, 60, 90, 120, 150, 180, 210, 240
Nine would have been tricky. Maybe just have used either 8 or 10 and call it close enough would be okay. And what to do when some of the points are negative?
I can see Excel tackles this problem nicely.
Does anyone know a general-purpose algorithm (even some brute force is okay) for solving this? I don't have to do it quickly, but it should look nice.
A long time ago I have written a graph module that covered this nicely. Digging in the grey mass gets the following:
Determine lower and upper bound of the data. (Beware of the special case where lower bound = upper bound!
Divide range into the required amount of ticks.
Round the tick range up into nice amounts.
Adjust the lower and upper bound accordingly.
Lets take your example:
15, 234, 140, 65, 90 with 10 ticks
lower bound = 15
upper bound = 234
range = 234-15 = 219
tick range = 21.9. This should be 25.0
new lower bound = 25 * round(15/25) = 0
new upper bound = 25 * round(1+235/25) = 250
So the range = 0,25,50,...,225,250
You can get the nice tick range with the following steps:
divide by 10^x such that the result lies between 0.1 and 1.0 (including 0.1 excluding 1).
translate accordingly:
0.1 -> 0.1
<= 0.2 -> 0.2
<= 0.25 -> 0.25
<= 0.3 -> 0.3
<= 0.4 -> 0.4
<= 0.5 -> 0.5
<= 0.6 -> 0.6
<= 0.7 -> 0.7
<= 0.75 -> 0.75
<= 0.8 -> 0.8
<= 0.9 -> 0.9
<= 1.0 -> 1.0
multiply by 10^x.
In this case, 21.9 is divided by 10^2 to get 0.219. This is <= 0.25 so we now have 0.25. Multiplied by 10^2 this gives 25.
Lets take a look at the same example with 8 ticks:
15, 234, 140, 65, 90 with 8 ticks
lower bound = 15
upper bound = 234
range = 234-15 = 219
tick range = 27.375
Divide by 10^2 for 0.27375, translates to 0.3, which gives (multiplied by 10^2) 30.
new lower bound = 30 * round(15/30) = 0
new upper bound = 30 * round(1+235/30) = 240
Which give the result you requested ;-).
------ Added by KD ------
Here's code that achieves this algorithm without using lookup tables, etc...:
double range = ...;
int tickCount = ...;
double unroundedTickSize = range/(tickCount-1);
double x = Math.ceil(Math.log10(unroundedTickSize)-1);
double pow10x = Math.pow(10, x);
double roundedTickRange = Math.ceil(unroundedTickSize / pow10x) * pow10x;
return roundedTickRange;
Generally speaking, the number of ticks includes the bottom tick, so the actual y-axis segments are one less than the number of ticks.
Here is a PHP example I am using. This function returns an array of pretty Y axis values that encompass the min and max Y values passed in. Of course, this routine could also be used for X axis values.
It allows you to "suggest" how many ticks you might want, but the routine will return
what looks good. I have added some sample data and shown the results for these.
#!/usr/bin/php -q
<?php
function makeYaxis($yMin, $yMax, $ticks = 10)
{
// This routine creates the Y axis values for a graph.
//
// Calculate Min amd Max graphical labels and graph
// increments. The number of ticks defaults to
// 10 which is the SUGGESTED value. Any tick value
// entered is used as a suggested value which is
// adjusted to be a 'pretty' value.
//
// Output will be an array of the Y axis values that
// encompass the Y values.
$result = array();
// If yMin and yMax are identical, then
// adjust the yMin and yMax values to actually
// make a graph. Also avoids division by zero errors.
if($yMin == $yMax)
{
$yMin = $yMin - 10; // some small value
$yMax = $yMax + 10; // some small value
}
// Determine Range
$range = $yMax - $yMin;
// Adjust ticks if needed
if($ticks < 2)
$ticks = 2;
else if($ticks > 2)
$ticks -= 2;
// Get raw step value
$tempStep = $range/$ticks;
// Calculate pretty step value
$mag = floor(log10($tempStep));
$magPow = pow(10,$mag);
$magMsd = (int)($tempStep/$magPow + 0.5);
$stepSize = $magMsd*$magPow;
// build Y label array.
// Lower and upper bounds calculations
$lb = $stepSize * floor($yMin/$stepSize);
$ub = $stepSize * ceil(($yMax/$stepSize));
// Build array
$val = $lb;
while(1)
{
$result[] = $val;
$val += $stepSize;
if($val > $ub)
break;
}
return $result;
}
// Create some sample data for demonstration purposes
$yMin = 60;
$yMax = 330;
$scale = makeYaxis($yMin, $yMax);
print_r($scale);
$scale = makeYaxis($yMin, $yMax,5);
print_r($scale);
$yMin = 60847326;
$yMax = 73425330;
$scale = makeYaxis($yMin, $yMax);
print_r($scale);
?>
Result output from sample data
# ./test1.php
Array
(
[0] => 60
[1] => 90
[2] => 120
[3] => 150
[4] => 180
[5] => 210
[6] => 240
[7] => 270
[8] => 300
[9] => 330
)
Array
(
[0] => 0
[1] => 90
[2] => 180
[3] => 270
[4] => 360
)
Array
(
[0] => 60000000
[1] => 62000000
[2] => 64000000
[3] => 66000000
[4] => 68000000
[5] => 70000000
[6] => 72000000
[7] => 74000000
)
Try this code. I've used it in a few charting scenarios and it works well. It's pretty fast too.
public static class AxisUtil
{
public static float CalculateStepSize(float range, float targetSteps)
{
// calculate an initial guess at step size
float tempStep = range/targetSteps;
// get the magnitude of the step size
float mag = (float)Math.Floor(Math.Log10(tempStep));
float magPow = (float)Math.Pow(10, mag);
// calculate most significant digit of the new step size
float magMsd = (int)(tempStep/magPow + 0.5);
// promote the MSD to either 1, 2, or 5
if (magMsd > 5.0)
magMsd = 10.0f;
else if (magMsd > 2.0)
magMsd = 5.0f;
else if (magMsd > 1.0)
magMsd = 2.0f;
return magMsd*magPow;
}
}
Sounds like the caller doesn't tell you the ranges it wants.
So you are free to changed the end points until you get it nicely divisible by your label count.
Let's define "nice". I would call nice if the labels are off by:
1. 2^n, for some integer n. eg. ..., .25, .5, 1, 2, 4, 8, 16, ...
2. 10^n, for some integer n. eg. ..., .01, .1, 1, 10, 100
3. n/5 == 0, for some positive integer n, eg, 5, 10, 15, 20, 25, ...
4. n/2 == 0, for some positive integer n, eg, 2, 4, 6, 8, 10, 12, 14, ...
Find the max and min of your data series. Let's call these points:
min_point and max_point.
Now all you need to do is find is 3 values:
- start_label, where start_label < min_point and start_label is an integer
- end_label, where end_label > max_point and end_label is an integer
- label_offset, where label_offset is "nice"
that fit the equation:
(end_label - start_label)/label_offset == label_count
There are probably many solutions, so just pick one. Most of the time I bet you can set
start_label to 0
so just try different integer
end_label
until the offset is "nice"
I'm still battling with this :)
The original Gamecat answer does seem to work most of the time, but try plugging in say, "3 ticks" as the number of ticks required (for the same data values 15, 234, 140, 65, 90)....it seems to give a tick range of 73, which after dividing by 10^2 yields 0.73, which maps to 0.75, which gives a 'nice' tick range of 75.
Then calculating upper bound:
75*round(1+234/75) = 300
and the lower bound:
75 * round(15/75) = 0
But clearly if you start at 0, and proceed in steps of 75 up to the upper bound of 300, you end up with 0,75,150,225,300
....which is no doubt useful, but it's 4 ticks (not including 0) not the 3 ticks required.
Just frustrating that it doesn't work 100% of the time....which could well be down to my mistake somewhere of course!
The answer by Toon Krijthe does work most of the time. But sometimes it will produce excess number of ticks. It won't work with negative numbers as well. The overal approach to the problem is ok but there is a better way to handle this. The algorithm you want to use will depend on what you really want to get. Below I'm presenting you my code which I used in my JS Ploting library. I've tested it and it always works (hopefully ;) ). Here are the major steps:
get global extremas xMin and xMax (inlucde all the plots you want to print in the algorithm )
calculate range between xMin and xMax
calculate the order of magnitude of your range
calculate tick size by dividing range by number of ticks minus one
this one is optional. If you want to have zero tick allways printed you use tick size to calculate number of positive and negative ticks. Total number of ticks will be their sum + 1 (the zero tick)
this one is not needed if you have zero tick allways printed. Calculate lower and upper bound but remember to center the plot
Lets start. First the basic calculations
var range = Math.abs(xMax - xMin); //both can be negative
var rangeOrder = Math.floor(Math.log10(range)) - 1;
var power10 = Math.pow(10, rangeOrder);
var maxRound = (xMax > 0) ? Math.ceil(xMax / power10) : Math.floor(xMax / power10);
var minRound = (xMin < 0) ? Math.floor(xMin / power10) : Math.ceil(xMin / power10);
I round minimum and maximum values to be 100% sure that my plot will cover all the data. It is also very important to floor log10 of range wheter or not it is negative and substract 1 later. Otherwise your algorithm won't work for numbers that are lesser than one.
var fullRange = Math.abs(maxRound - minRound);
var tickSize = Math.ceil(fullRange / (this.XTickCount - 1));
//You can set nice looking ticks if you want
//You can find exemplary method below
tickSize = this.NiceLookingTick(tickSize);
//Here you can write a method to determine if you need zero tick
//You can find exemplary method below
var isZeroNeeded = this.HasZeroTick(maxRound, minRound, tickSize);
I use "nice looking ticks" to avoid ticks like 7, 13, 17 etc. Method I use here is pretty simple. It is also nice to have zeroTick when needed. Plot looks much more professional this way. You will find all the methods at the end of this answer.
Now you have to calculate upper and lower bounds. This is very easy with zero tick but requires a little bit more effort in other case. Why? Because we want to center the plot within upper and lower bound nicely. Have a look at my code. Some of the variables are defined outside of this scope and some of them are properties of an object in which whole presented code is kept.
if (isZeroNeeded) {
var positiveTicksCount = 0;
var negativeTickCount = 0;
if (maxRound != 0) {
positiveTicksCount = Math.ceil(maxRound / tickSize);
XUpperBound = tickSize * positiveTicksCount * power10;
}
if (minRound != 0) {
negativeTickCount = Math.floor(minRound / tickSize);
XLowerBound = tickSize * negativeTickCount * power10;
}
XTickRange = tickSize * power10;
this.XTickCount = positiveTicksCount - negativeTickCount + 1;
}
else {
var delta = (tickSize * (this.XTickCount - 1) - fullRange) / 2.0;
if (delta % 1 == 0) {
XUpperBound = maxRound + delta;
XLowerBound = minRound - delta;
}
else {
XUpperBound = maxRound + Math.ceil(delta);
XLowerBound = minRound - Math.floor(delta);
}
XTickRange = tickSize * power10;
XUpperBound = XUpperBound * power10;
XLowerBound = XLowerBound * power10;
}
And here are methods I mentioned before which you can write by yourself but you can also use mine
this.NiceLookingTick = function (tickSize) {
var NiceArray = [1, 2, 2.5, 3, 4, 5, 10];
var tickOrder = Math.floor(Math.log10(tickSize));
var power10 = Math.pow(10, tickOrder);
tickSize = tickSize / power10;
var niceTick;
var minDistance = 10;
var index = 0;
for (var i = 0; i < NiceArray.length; i++) {
var dist = Math.abs(NiceArray[i] - tickSize);
if (dist < minDistance) {
minDistance = dist;
index = i;
}
}
return NiceArray[index] * power10;
}
this.HasZeroTick = function (maxRound, minRound, tickSize) {
if (maxRound * minRound < 0)
{
return true;
}
else if (Math.abs(maxRound) < tickSize || Math.round(minRound) < tickSize) {
return true;
}
else {
return false;
}
}
There is only one more thing that is not included here. This is the "nice looking bounds". These are lower bounds that are numbers similar to the numbers in "nice looking ticks". For example it is better to have the lower bound starting at 5 with tick size 5 than having a plot that starts at 6 with the same tick size. But this my fired I leave it to you.
Hope it helps.
Cheers!
Converted this answer as Swift 4
extension Int {
static func makeYaxis(yMin: Int, yMax: Int, ticks: Int = 10) -> [Int] {
var yMin = yMin
var yMax = yMax
var ticks = ticks
// This routine creates the Y axis values for a graph.
//
// Calculate Min amd Max graphical labels and graph
// increments. The number of ticks defaults to
// 10 which is the SUGGESTED value. Any tick value
// entered is used as a suggested value which is
// adjusted to be a 'pretty' value.
//
// Output will be an array of the Y axis values that
// encompass the Y values.
var result = [Int]()
// If yMin and yMax are identical, then
// adjust the yMin and yMax values to actually
// make a graph. Also avoids division by zero errors.
if yMin == yMax {
yMin -= ticks // some small value
yMax += ticks // some small value
}
// Determine Range
let range = yMax - yMin
// Adjust ticks if needed
if ticks < 2 { ticks = 2 }
else if ticks > 2 { ticks -= 2 }
// Get raw step value
let tempStep: CGFloat = CGFloat(range) / CGFloat(ticks)
// Calculate pretty step value
let mag = floor(log10(tempStep))
let magPow = pow(10,mag)
let magMsd = Int(tempStep / magPow + 0.5)
let stepSize = magMsd * Int(magPow)
// build Y label array.
// Lower and upper bounds calculations
let lb = stepSize * Int(yMin/stepSize)
let ub = stepSize * Int(ceil(CGFloat(yMax)/CGFloat(stepSize)))
// Build array
var val = lb
while true {
result.append(val)
val += stepSize
if val > ub { break }
}
return result
}
}
this works like a charm, if you want 10 steps + zero
//get proper scale for y
$maximoyi_temp= max($institucion); //get max value from data array
for ($i=10; $i< $maximoyi_temp; $i=($i*10)) {
if (($divisor = ($maximoyi_temp / $i)) < 2) break; //get which divisor will give a number between 1-2
}
$factor_d = $maximoyi_temp / $i;
$factor_d = ceil($factor_d); //round up number to 2
$maximoyi = $factor_d * $i; //get new max value for y
if ( ($maximoyi/ $maximoyi_temp) > 2) $maximoyi = $maximoyi /2; //check if max value is too big, then split by 2
The above algorithms do not take into consideration the case when the range between min and max value is too small. And what if these values are a lot higher than zero? Then, we have the possibility to start the y-axis with a value higher than zero. Also, in order to avoid our line to be entirely on the upper or the down side of the graph, we have to give it some "air to breathe".
To cover those cases I wrote (on PHP) the above code:
function calculateStartingPoint($min, $ticks, $times, $scale) {
$starting_point = $min - floor((($ticks - $times) * $scale)/2);
if ($starting_point < 0) {
$starting_point = 0;
} else {
$starting_point = floor($starting_point / $scale) * $scale;
$starting_point = ceil($starting_point / $scale) * $scale;
$starting_point = round($starting_point / $scale) * $scale;
}
return $starting_point;
}
function calculateYaxis($min, $max, $ticks = 7)
{
print "Min = " . $min . "\n";
print "Max = " . $max . "\n";
$range = $max - $min;
$step = floor($range/$ticks);
print "First step is " . $step . "\n";
$available_steps = array(5, 10, 20, 25, 30, 40, 50, 100, 150, 200, 300, 400, 500);
$distance = 1000;
$scale = 0;
foreach ($available_steps as $i) {
if (($i - $step < $distance) && ($i - $step > 0)) {
$distance = $i - $step;
$scale = $i;
}
}
print "Final scale step is " . $scale . "\n";
$times = floor($range/$scale);
print "range/scale = " . $times . "\n";
print "floor(times/2) = " . floor($times/2) . "\n";
$starting_point = calculateStartingPoint($min, $ticks, $times, $scale);
if ($starting_point + ($ticks * $scale) < $max) {
$ticks += 1;
}
print "starting_point = " . $starting_point . "\n";
// result calculation
$result = [];
for ($x = 0; $x <= $ticks; $x++) {
$result[] = $starting_point + ($x * $scale);
}
return $result;
}
For anyone who need this in ES5 Javascript, been wrestling a bit, but here it is:
var min=52;
var max=173;
var actualHeight=500; // 500 pixels high graph
var tickCount =Math.round(actualHeight/100);
// we want lines about every 100 pixels.
if(tickCount <3) tickCount =3;
var range=Math.abs(max-min);
var unroundedTickSize = range/(tickCount-1);
var x = Math.ceil(Math.log10(unroundedTickSize)-1);
var pow10x = Math.pow(10, x);
var roundedTickRange = Math.ceil(unroundedTickSize / pow10x) * pow10x;
var min_rounded=roundedTickRange * Math.floor(min/roundedTickRange);
var max_rounded= roundedTickRange * Math.ceil(max/roundedTickRange);
var nr=tickCount;
var str="";
for(var x=min_rounded;x<=max_rounded;x+=roundedTickRange)
{
str+=x+", ";
}
console.log("nice Y axis "+str);
Based on the excellent answer by Toon Krijtje.
This solution is based on a Java example I found.
const niceScale = ( minPoint, maxPoint, maxTicks) => {
const niceNum = ( localRange, round) => {
var exponent,fraction,niceFraction;
exponent = Math.floor(Math.log10(localRange));
fraction = localRange / Math.pow(10, exponent);
if (round) {
if (fraction < 1.5) niceFraction = 1;
else if (fraction < 3) niceFraction = 2;
else if (fraction < 7) niceFraction = 5;
else niceFraction = 10;
} else {
if (fraction <= 1) niceFraction = 1;
else if (fraction <= 2) niceFraction = 2;
else if (fraction <= 5) niceFraction = 5;
else niceFraction = 10;
}
return niceFraction * Math.pow(10, exponent);
}
const result = [];
const range = niceNum(maxPoint - minPoint, false);
const stepSize = niceNum(range / (maxTicks - 1), true);
const lBound = Math.floor(minPoint / stepSize) * stepSize;
const uBound = Math.ceil(maxPoint / stepSize) * stepSize;
for(let i=lBound;i<=uBound;i+=stepSize) result.push(i);
return result;
};
console.log(niceScale(15,234,6));
// > [0, 100, 200, 300]
Based on #Gamecat's algorithm, I produced the following helper class
public struct Interval
{
public readonly double Min, Max, TickRange;
public static Interval Find(double min, double max, int tickCount, double padding = 0.05)
{
double range = max - min;
max += range*padding;
min -= range*padding;
var attempts = new List<Interval>();
for (int i = tickCount; i > tickCount / 2; --i)
attempts.Add(new Interval(min, max, i));
return attempts.MinBy(a => a.Max - a.Min);
}
private Interval(double min, double max, int tickCount)
{
var candidates = (min <= 0 && max >= 0 && tickCount <= 8) ? new[] {2, 2.5, 3, 4, 5, 7.5, 10} : new[] {2, 2.5, 5, 10};
double unroundedTickSize = (max - min) / (tickCount - 1);
double x = Math.Ceiling(Math.Log10(unroundedTickSize) - 1);
double pow10X = Math.Pow(10, x);
TickRange = RoundUp(unroundedTickSize/pow10X, candidates) * pow10X;
Min = TickRange * Math.Floor(min / TickRange);
Max = TickRange * Math.Ceiling(max / TickRange);
}
// 1 < scaled <= 10
private static double RoundUp(double scaled, IEnumerable<double> candidates)
{
return candidates.First(candidate => scaled <= candidate);
}
}
A demo of accepted answer
function tickEvery(range, ticks) {
return Math.ceil((range / ticks) / Math.pow(10, Math.ceil(Math.log10(range / ticks) - 1))) * Math.pow(10, Math.ceil(Math.log10(range / ticks) - 1));
}
function update() {
const range = document.querySelector("#range").value;
const ticks = document.querySelector("#ticks").value;
const result = tickEvery(range, ticks);
document.querySelector("#result").textContent = `With range ${range} and ${ticks} ticks, tick every ${result} for a total of ${Math.ceil(range / result)} ticks at ${new Array(Math.ceil(range / result)).fill(0).map((v, n) => Math.round(n * result)).join(", ")}`;
}
update();
<input id="range" min="1" max="10000" oninput="update()" style="width:100%" type="range" value="5000" width="40" />
<br/>
<input id="ticks" min="1" max="20" oninput="update()" type="range" style="width:100%" value="10" />
<p id="result" style="font-family:sans-serif"></p>

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