i need to how parabola is drawn using midpoint algorithm. i got how to obtain the circle and line and also ellipse but couldn't get proper method for parabola. can anyone help me out for doing it from beginning to end.
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Given two points and a control point, one can easily draw a bezier path between the two points. What I would like to do use a bezier curve to draw a path that with changing width, by a assigning a "weight" to a the points of the curve which will determine its width. For example, if I give weight=0 to the first point of the curve and weight = 1 to the second point of the curve then something like the following path should be generated (the curve in the picture is cubic, but I am working with quadratic bezier curves):
In order to do this I would need to find the control points of the "edge" curves that determine the shape and then fill the shape that is found between the two new curves. However, I am quite unsure on how this can be done. One thing I thought about was to determine the starting and ending points of the new curves by simple drawing perpendicular segments to the line connecting the original control point and the original end points, but this still doesn't solve the problem of finding the new control points for the new curves.
I would use cubics instead of quadratics.
Yes you offset the control points perpendicularly by your weight but not the control points of BEZIER but control points of interpolation cubic (or catmull-rom) and then just convert that into Bezier control points. See related QAs:
How can i produce multi point linear interpolation?
How to create bezier curves for an arc with different start and end tangent slopes
draw outline for some connected lines
However much easier would be to directly render curve using Shaders and (perpendicular) distance. See:
Draw Quadratic Curve on GPU
That way you would not need to offset anything just interpolate the width of your curve ...
Maybe this could help, also there is an example on variable offseting
https://microbians.com/mathcode
I'm confused in using geometry shader for solve this problem:
I have two radius of a circle that every radius is a line and I called that's a line. every line is made of list of points that every points have a color.
so how fill between two lines with lines that's color of every point on a line has between colors of points of two lines on a equal radius.
it is so may be complex so I show it with a picture:
gradient Radiuses
.
I think best way of solving this problem is geometry shader but if you know better way that have good performance, I listen.
thanks.
I'm trying to infer an object's direction of movement using dense optical flow in OpenCV. I'm using calcOpticalFlowFarneback() to get flow coordinates and cartToPolar() to acquire vector angles which would indicate direction.
To interpret the results I need to know the reference point for measuring the angle. I have found this blog post indicating that the range of angles is 360°. That tells me that the angle measurement would go along the lines of the unit circle. I couldn't make out much more than that.
The documentation for cartToPolar() doesn't cover this and my attempts at testing it have failed.
It seems that the angle produced by cartToPolar() is in reference to the unit circle rotated clockwise by 90° centered on the image coordinate starting point in the top left corner. It would look like this.
I came to this conclusion by using the dense optical flow example provided by OpenCV. I replaced the line hsv[...,0] = ang*180/np.pi/2 with hsv[...,0] = ang*180/np.pi to get correct angle conversion from radians. Then I tested a video with people moving from top right to bottom left and vice versa. I sampled the dominant color with GIMP and got RGB values which I converted to HSV values. Hue value corresponds to the angle in degrees.
People moving from top right to bottom left produced an angle of about 300° and people moving the other way round produced an angle of about 120°. This hinted at the way the unit circle is positioned.
Looking at the code, fastAtan32f is used to compute the angles. and that seems to be a atan2 implementation.
I have two objects: A sphere and an object. Its an object that I created using surface reconstruction - so we do not know the equation of the object. I want to know the intersecting points on the sphere when the object and the sphere intersect. If we had a sphere and a cylinder, we could solve for the equation and figure out the area and all that but the problem here is that the object is not uniform.
Is there a way to find out the intersecting points or area on the sphere?
I'd start by finding the intersection of triangles with the sphere. First find the intersection of each triangle's plane and the sphere, which gives a circle. Then find the circle's intersection/s with the triangle edges in 2D using line/circle tests. The result will be many arcs which I guess you could approximate with lines. I'm not really sure where to go from here without knowing the end goal.
If it's surface area you're after, maybe a numerical approach would be better. I'd cover the sphere in points and count the number inside the non-uniform object. To find if a point is inside, maybe trace outwards and count the intersections with the surface (if it's odd, the point is inside). You could use the stencil buffer for this if you wanted (similar to stencil shadows).
If you want the volume of intersection a quick google search gives "carve", a mesh based CSG library.
Starting with triangles versus the sphere will give you the points of intersection.
You can take the arcs of intersection with each surface and combine them to make fences around the sphere. Ideally your reconstructed object will be in winged-edge format so you could just step from one fence segment to the next, but with reconstructed surfaces I guess you might need to apply some slightly fuzzy logic.
You can determine which side of each fence is inside the reconstructed object and which side is out by factoring in the surface normals along the fence.
You can then cut the sphere along the fences and add the internal bits to the display.
For the other side of things you could remove any triangle completely inside the sphere and cut those that intersect.
I have a rotate rectangle and I know the size of the diagonal. I also know the angle used to rotate the rectangle.
How can I calculate the width and height of the rectangle?
For a sketch of the problem, see:
1) create a new line starting at one of the end-points of the diagonal and travelling at the rotation angle.
2) project the other diagonal terminus onto this line. You now know one side of the rectangle.
3) Copy the segment to the other side of the diagonal and connect the endpoints to complete the rectangle.
The only 'tricky' code here is the projection. This webpage has some example code for Point-Line distance/projection: http://softsurfer.com/Archive/algorithm_0102/algorithm_0102.htm
Thanks David Rutten,
I got it working. Your site about the projection was to much for my math knowledge, but with some google i find a nice point to line intersection function which helped me to calc the length (distance) of one of the sides.
Unfortunately I'm too "new" here to award you with credits or reply on your anwser.
#Eric bainville: I knew the distance because i had point1 and point2 (upper left and bottom right) coordinates. With those coordinates it is possible. I didnt mention this, but luckily David guessed right that I knew them.
Thanks again!