How to plot (x^2+y^2-1)^3=x^2*y^3? - inkscape

I knew the function plotter,but it seemed no way to plot (x^2+y^2-1)^3=x^2*y^3.
I am new to inkscape, thanks for any answer in advance!

Do you need exact function or just heart shape? Try to use Parametric Curves Extension with next formulas: X-Function 16*sin(t)**3, Y-Function: 13*cos(t)-5*cos(2*t)-2*cos(3*t)-cos(4*t)
Here is result:

Related

How to scale/rotate/move an asset in OpenSceneGraph

I am totally new with OpenSceneGraph
I can open and save an OSG asset.
I need to do some simple transformations on it, like dimension scaling/rotation/translation.
It seems a pretty easy task, anyway I can't find any quick documentation :/
osg::ref_ptr<osg::Node> rectangle = osgDB::readNodeFile("../../inputs/Rectangle.osg");
// define simple transformation matrix
// apply simple trnasformation matrix
osgDB::writeNodeFile(*rectangle, "../../outputs/saved.osg");
Any hint?
Use class osg::MatrixTransform, see for instance this example

why python cv2.drawContours() just draw the first contours?

I am having trouble filling a mask using cv2.drawContours, I dont know what could it be, or how to fix it.
I have a list with three elements's sublists [coordX,coordY, contour], so for every pair of coordinates, there is an if/else decision, each one with this stament: cv2.drawContours(mask,[l1[0][2]],0,c1[cla],-1)
[l1[0][2]]: contour, like array([[[437, 497]],[[436, 498]],[[439, 498]], [[438, 497]]])
c1[cla]: tuple, like (25,250,138)
The script runs well without errors, but the resulting image is almost black, just having 4 green pixels.
Any suggestion or advice?
Finally, I found what was the problem. I was passing the same contour to every step ([l1[0][2]]), so I need to change to operate with index, like [l1[i][2]]).
Sorry for that mistake and for your patience.
Have a good day, Jaime

Refining Camera parameters and calculating errors - OpenCV

I've been trying to refine my camera parameters with CvLevMarq but after reading about it, it seems to be causing mixed results - which is exactly what I am experiencing. I read about the alternatives and came upon EIGEN - and also found this library that utilizes it.
However, the library above seems to use a stitching class that doesn't support OpenCV and will probably require me to port it to OpenCV.
Before going ahead and doing so, which will probably not be an easy task, I figured I'd ask around first and see if anyone else had the same problem?
I'm currently using:
1. Calculating features with FASTFeatureDetector
Ptr<FeatureDetector> detector = new FastFeatureDetector(5,true);
detector->detect(firstGreyImage, features_global[firstImageIndex].keypoints); // Previous picture
detector->detect(secondGreyImage, features_global[secondImageIndex].keypoints); // New picture
2. Extracting features with SIFTDescriptorExtractor
Ptr<SiftDescriptorExtractor> extractor = new SiftDescriptorExtractor();
extractor->compute(firstGreyImage, features_global[firstImageIndex].keypoints, features_global[firstImageIndex].descriptors); // Previous Picture
extractor->compute(secondGreyImage, features_global[secondImageIndex].keypoints, features_global[secondImageIndex].descriptors); // New Picture
3. Matching features with BestOf2NearestMatcher
vector<MatchesInfo> pairwise_matches;
BestOf2NearestMatcher matcher(try_use_gpu, 0.50f);
matcher(features_global, pairwise_matches);
matcher.collectGarbage();
4. CameraParams.R quaternion passed from a device (slightly inaccurate which causes the issue)
5. CameraParams.Focal == 389.0f -- Played around with this value, 389.0f is the only value that matches the images horizontally but not vertically.
6. Bundle Adjustment (cvLevMarq, calcError & calcJacobian)
Ptr<BPRefiner> adjuster = new BPRefiner();
adjuster->setConfThresh(0.80f);
adjuster->setMaxIterations(5);
(*adjuster)(features,pairwise_matches,cameras);
7. ExposureCompensator (GAIN)
8. OpenCV MultiBand Blender
What works so far:
SeamFinder - works to some extent but it depends on the result of the cvLevMarq algoritm. I.e. if the algoritm is off, seamFinder is going to be off too.
HomographyBasedEstimator works beautifully. However, since it "relies" on the features, it's unfortunately not the method that I'm looking for.
I wouldn't want to rely on the features since I already have the matrix, if there's a way to "refine" the current matrix instead - then that would be the targeted result.
Results so far:
cvLevMarq "Russian roulette" 6/10:
This is what I'm trying to achieve 10/10 times. But 4/10 times, it looks like the picture below this one.
By simply just re-running the algorithm, the results change. 4/10 times it looks like this (or worse):
cvLevMarq "Russian roulette" 4/10:
Desired Result:
I'd like to "refine" my camera parameters with the features that I've matched - in hope that the images would align perfectly. Instead of hoping that cvLevMarq will do the job for me (which it won't 4/10 times), is there another way to ensure that the images will be aligned?
Update:
I've tried these versions:
OpenCV 3.1: Using CVLevMarq with 3.1 is like playing Russian roulette. Some times it can align them perfectly, and other times it estimates focal as NAN which causes segfault in the MultiBand Blender (ROI = 0,0,1,1 because of NAN)
OpenCV 2.4.9/2.4.13: Using CvLevMarq with 2.4.9 or 2.4.13 is unfortunately the same thing minus the NAN issue. 6/10 times it can align the images perfectly, but the other 4 times it's completely off.
My Speculations / Thoughts:
Template Matching using OpenCV. Maybe if I template match the ends of the images (i.e. x = 0, y = 0,height = image.height, width = 50). Any thoughts about this?
I found this interesting paper about Levenberg Marquardt applied in Homography. That looks like something that could solve my problem since the paper uses corner detection and whatnot to detect the features in the images. Any thoughts about this?
Maybe the problem isn't in CvLevMarq but instead in BestOf2NearestMatcher? However, I've searched for days and I couldn't find another method that returns the pairwise matches to pass to BPRefiner.
Hough Line Transform Detecting the lines in the first/second image and use that to align the images. Any thoughts on this? -- One thing might be, what if the images doesn't have any lines? I.e. empty wall?
Maybe I'm overkilling something so simple.. Or maybe I'm not? Basically, I'm trying to align a set of images so I can warp them without overlapping each-other. Drop a comment if it doesn't make sense :)
Update Aug 12:
After trying all kinds of combinations, the absolute best so far is CvLevMarq. The only problem with it is the mixed results shown in the images above. If anyone has any input, I'd be forever grateful.
It seems your parameter initialization is the problem. I would use a linear estimator first, i.e. ignore your noisy sensor, and then use this as the initial values for the non-linear optimizer.
A quick method is to use getaffinetransform, as you have mostly rotation.
Maybe you want to take a look at this library: https://github.com/ethz-asl/kalibr.
Cheers
If you want to stitch the images, you should see stitching_detailed.cpp. It will probably solve your problem.
In addition, I have used Graph Cut Seam Finding method with Canny Edge Detection for better stitching results in this code. If you want to optimize this code, see here.
Also, if you are going to use it for personal use, SIFT is good. You should know, SIFT is patented and will cost you if you use it for commercial purposes. Use ORB instead.
Hope it helps!

Convert HEALPix to cube map

I'm looking for a way to convert fits file using the HEALPix projection to a cube map. I'm particularly interested in converting files from the Planck data release.
My question in pictures:
I have:
I want:
I found a workaround using a function from CMBView: http://code.google.com/p/cmbview/source/browse/src/Classes/CMBdata.m
Result:
https://github.com/hannorein/planck_cmb_cubemaps

Perlin's Noise with OpenGL

I was studying Perlin's Noise through some examples # http://dindinx.net/OpenGL/index.php?menu=exemples&submenu=shaders and couldn't help to notice that his make3DNoiseTexture() in perlin.c uses noise3(ni) instead of PerlinNoise3D(...)
Now why is that? Isn't Perlin's Noise supposed to be a summation of different noise frequencies and amplitudes?
Qestion 2 is what does ni, inci, incj, inck stand for? Why use ni instead of x,y coordinates? Why is ni incremented with
ni[0]+=inci;
inci = 1.0 / (Noise3DTexSize / frequency);
I see Hugo Elias created his Perlin2D with x,y coordinates, and so does PerlinNoise3D(...).
Thanks in advance :)
I now understand why and am going to answer my own question in hopes that it helps other people.
Perlin's Noise is actually a synthesis of gradient noises. In its production process, we must compute the dot product of a vector pointing from one of the corners flooring the input point to the input point itself with the random-generated gradient vector.
Now if the input point were a whole number, such as the xyz coordinates of a texture you want to create, the dot product would always return 0, which would give you a flat noise. So instead, we use inci, incj, inck as an alternative index. Yep, just an index, nothing else.
Now returning to question 1, there are two methods to implement Perlin's Noise:
1.Calculate the noise values separately and store them in the RGBA slots in the texture
2.Synthesize the noises up before-hand and store them in one of the RGBA slots in the texture
noise3(ni) is the actual implementation of method 1, while PerlinNoise3D(...) suggests the latter.
In my personal opinion, method 1 is much better because you have much more flexibility over how you use each octave in your shaders.
My guess on the reason for using noise3(ni) in make3DNoiseTexture() instead if PerlinNoise3D(...) is that when you use that noise texture in your shader you want to be able to replicate and modify the functionality of PerlinNoise3D(...) directly in the shader.
My guess for the reasoning behind ni, inci, incj, inck is that using x,y,z of the volume directly don't give a good result so by scaling the the noise with the frequency instead it is possible to adjust the resolution of the noise independently from the volume size.