I'm trying to draw a flat surface out of voxels, the goal is to draw it filled and I'm having a lot of trouble. Everything I try results in holes on the surface. The surface has 4 corners, but I'd like to be able to use the same method for triangles too.
Here's what I've tried:
Draw along from one parallel side to the other
Draw only in one direction (z direction) along a side of the plane
I've had the most success with 2 but it fails when I add any pitch or roll to the plane (any elevation present).
Any tips? There's no code because I'm sure my implementations are all correct, it's just the choice of algorithm that's wrong.
EDIT:
On a side note, though number 2 had less holes, the planes were distorted and didn't appear flat.
EDIT2:
I'm sticking with my first decision, but now the question is, how do I detect when there will be a hole? By observation I notice there's the same amount of holes per plane regardless of pitch and roll. Yaw is the culprit here.
EDIT3:
I'm leaving this question up but I decided to just test a nearby block to see if it's empty. I didn't want to do it, but yeah. If you have a more elegant solution I'm all ears.
A plane, being infinite, does not have corners. Are you talking about a four-sided polygon? Does it have square corners?
For a polygon, I would certainly start off with a triangle, since you can construct any other polygon out of triangles, not the other way around.
Then, a good start for filling a triangle would probably be to come up with an accurate test of whether a given voxel should be filled or not. Here's an example of two different point-in-triangle tests.
After you have that you can proceed in different ways. For example, although not the most efficient, you could region-grow from the center, testing each neighboring voxel and recursing with a stack.
Related
At the moment I have a simple animation where a car (JPanel) approaches a junction where after it waits for traffic lights to turn green and continues straight on. However I'm going to the next step now where I want the car to turn 90 deg right in a smooth curve to turn onto the perpendicular road. I have sketched roughly how it looks and the curve represent the way I want the car to turn:
I'm not too sure how to do this. I suppose I would need to represent some sort of bezier curve? Or matrix transformation to rotate the car?
Can someone give advice on the best way to do this in Swing.
If you are new to graphics in Java, I recommend this tutorial. If I were to code what you are doing, I see two options.
First and easiest, you can model turning as "first driving straight, then turning 90º along the edge of a circle centred on the corner I am turning around, and then driving straight again". The easiest way to do this is to define a JPanel that draws your Image (yes, a JPanel; if you don't paint their background, you can layer JPanels on top of each other - and they will be painted in the correct order; make the background JPanel opaque so that it cleans up before drawing the next frame), and give it an AffineTransform that makes the image display in the position you want it to. You will need to adjust the increments in the transform so that the speed appears constant; trial and error, or a bit of geometry (90º of radius R implies R*pi/2.0 total travel along the curved path) , will help you out there.
The hard way is to consider the car's route to be an arbitrary Shape (which you can define using Bezier curves, for example), extract a flattened PathIterator from it, advance in equally-spaced jumps along that iterator, and calculate the rotation you need from the position along the curve and the heading at any given point (you can estimate the heading by taking 2 successive samples, and aligning the car according to these samples). This is harder than using the above method, but allows your car to follow arbitrarily complex paths.
I currently have an arraylist of points from a freehand drawing on a canvas. I was wondering if there is a simple algorithm to detect if that shape represents a circle.I have already researched this a little and the main items I am pointed at are either the Hough transform or having bitmap images but both of these seem a little over the top for what I need it for. Any pointers to algorithms or implementation would be very helpful.
thanks in advance sansoms,
If I interpret your question correctly, you want to know if all the points are on a circle.
As illustrated in the picture, we pick three points A, B, C from the list and compute the origin O of the presumed circle. By checking the distance between O and each point from the list, we can conclude whether these points are on a circle.
If you do not know what the user wanted to draw (e.g., a circle, an ellipse, a line, or a rectangle), you could use some basic optimization algorithm to find the shape best matching the hand-drawn points.
for each basic shape (oval, rectangle, triangle, line, etc.), create a random instance of that shape and measure the error w.r.t. the given points
optimize each of the shapes (individually) until you have the oval best matching the given points, the rectangle best matching the points, the best triangle, etc.
pick the shape that has the lowest error and draw it
Maybe this answer can give you some ideas: https://stackoverflow.com/a/940041/12860
In short: calculate the second derivative. If it is quite constand, it is probably a circle.
Reading your comment, an easier method to draw a circle is for the user to click the center point, then drag the radius of the circle. It's a lot less calculation, and easier for the user to draw.
You can do the same thing with a rectangle, or any other convex polygon.
I made a program in Java where circles can bounce into each other and gravitate towards each other.
For the most part (few circles on the screen), there are no noticeable bugs. The problem starts to happen when there is a large amount of circles on screen. Sometimes, the circles will overlap if it gets too crowded. It's as if the weight of all the other circles are crushing the circles together, causing them to overlap. Of course, there program doesn't know anything about how much a circle weighs, so it's not really crushing. Most likely, the piece of logic that handles resolving collisions is not able to handle crowded situations.
Circles are stored in an array, and each circle goes through the array using a for loop, comparing itself to the other circles. If the distance between the center of this circle and the center of the other circle is less than the sum of their radii, then the circles are colliding. The velocities of both circles are updated using an equation for collisions.
I think the problem occurs because if a circle is surrounded, it might receive an updated velocity into the circle behind it, while the circle behind it also receives an updated velocity into the former circle. In other words, the two circles get told to move toward each other, even though they are already touching. Once they overlap this way, I don't know why they don't undo their overlap.
I've tried restoring touching scenario if they are overlapping by finding the distance they are overlapped, then moving them apart from each other; each moves half the overlap distance apart. This doesn't change the circle's velocity, only their position.
This still doesn't solve the problem. If the circle is surrounded, and it overlaps with one of it's neighboring circles, its position is changed so they aren't overlapping, but this new position may cause it to overlap with another circle. Same problem.
If there was no gravity pushing the circles together, they would eventually spread out and resolve their overlapping issues, but the gravity prevents this from happening.
Further information:
Gravity is not taken into account when calculating new velocities after a collision.
Sounds like your hunches about what is causing the problem are correct in both cases.
Unfortunately, there's no easy way to fix this issue - it pretty much means rewriting your whole collision detection & resolution code from scratch. You have to work out the exact timing of the first collision, update everything only that far, resolve the collision (do your velocity update) then work out the exact timing of the next collision, then repeat...
Writing a good physics engine is hard, there's a good reason that there are many textbooks on the market about this subject!
The cheap 'fix' for your problem is to reduce the time interval for updates - e.g. instead of updating the physics in 33ms steps (~30fps), try updating in 16ms steps (~60fps). This won't prevent the problem, but it will make it much less likely to occur. Halving the time step will also double the time the processor has to spend doing physics updates!
If you use the cheap fix, the time step which will work best for you will be determined by how frequently collisions occur - more collisions means smaller time steps. How frequently collisions occur basically depends on how fast the circles tend to move and their population density (how much of a given area is filled by circles).
UPDATE: A little more info on the 'proper' approach.
The update would go something like this:
Start updating a frame. Let's say we want to update as far as time tF.
For every pair of circles, work out when you would expect a collision to occur (ignoring all the other circles). Let's call this time tC.
Find the smallest value of tC. Let's say this is for the collision between circles A and B, and let's call that collision cAB.
If tC <= tF, update all of the circles up to time tC. Otherwise, go to step 6.
Resolve collision cAB. Go back to step 2!
Update all the circles to time tF.
As you might imagine, this can get quite complicated. Step 2 can be quite tricky (and coputationally expensive) for non-circular objects (especially once you include things like angular momentum, etc.) although there are a lot of tricks you can do here to speed it up. It's also basically impossible to know how many times you'll be looping between steps 2 and 5.
Like I said, doing good physics simulation is hard. Doing it in real-time is even harder!
My question is, will the code given in http://pietschsoft.com/post/2008/07/Virtual-Earth-Polygon-Search-Is-Point-Within-Polygon.aspx work to find a point in one of areas mentioned in
below file (page 7-9):
http://www.weather.gov/directives/sym/pd01008006curr.pdf
looking forward,
A point-in-polygon algorithm usually just counts the number of times it crosses a line by "drawing" one out in any particular direction. It would then know if it's in the polygon or not by knowing how many times it crossed that line (even number it was outside, odd number it is inside). The code on that site looks like it just flips a boolean instead of adding to a counter but it's the same thing.
I must confess I have not read the PDF you linked too (too long!) but I've not come across an instance where the algorithm fails.
One tip might be to draw a rough square around the outermost extremeties of the polygon first and check whether it falls within that to avoid having to test each point).
I believe it will fail in some cases. The algorithm you linked to, which is correct for planar geometry, is incorrect for spherical geometry. Consider the rectangles which cross the 180th meridian, e.g. the rectangle labelled "M". The algorithm would consider that rectangle as covering the americas, Africa, and Europe, but not Asia or the Pacific.
I'm currently writing an application that actually acts as a "cut" tool for 3D meshes. Well, I had some problems with it now which I am clueless on how to solve, since it is my first application.
I have loaded a model from an object file onto the canvas, then on the same canvas, I use the mouse drag event to draw lines to define the cutting point.
Let us say I want to cut a ball into half and I draw the line in the middle. How do I detect the vertices of the ball under the line.
Secondly, if I rotate/translate the ball, would all the the vertices information change?
Think of what you'd do in the real world: You can't cut a ball with a line, you must use a knife (a line has no volume). To cut the ball, you must move the knife through the ball.
So what you're looking after is a plane, not a line. To get such a plane, you must use some 3D math. What you have is the canvas orientation and the "side view" of the plane (which looks like a line).
So the plane you're looking for is perpendicular to the canvas. A simple way to get such a plane is to take the canvas orientation and create a plane which has the same orientation and then rotate the plane around the line by 90°.
After that, you can visit all edges of your model and determine on which side of the plane they are. For this, determine on which side of the plane the end points of the edge are. Use the cross product. If they are on the same side (both results of the cross products will have the same sign), you can ignore the edge. Otherwise, you need to determine the intersection point of the edge and plane. Create new edges and connect them accordingly.
See this page for some background on the math. But you should find some helper methods for all this in your opengl library.
if I rotate / translate the ball, would all the the vertices information change
Of course.
It's not going to be that easy.
I assume the line you are drawing induces a plane which then cuts the sphere.
To do so, you have to calculate the intersecting area of the sphere and the plane.
This is not a trivial task and I suggest using an existing framework for this or if you really want to do this yourself, read about basic intersection problems to get a feeling for this kind of problem. This paper offers a good introduction to various intersection tests.
In general boundary represended volumes, as in your case, are difficult to handle when it comes to more advanced manipulations. Cutting a sphere in half is easy compared to burring a small hole into it. Sometimes it's better to use a volume representation, like tetrahedral meshes or CSG.
Regarding your second question, you shouldn't rotate or translate the sphere, rotate and translate the camera.