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Java how to draw and fill a Polygon which has holes

I am currently trying to draw and fill a Polygon which has a hole in it in Java. Normally this would not be a big problem, since I would draw the exterior ring and then draw the interior ring with the color of the background.
But the problem is, that the polygon is displayed above a image which should be "seen" through the hole.
I am writing the code in Java and am using JTS Topology Suite for my geometry data.
This is my current code, which just paints the border and fills the polygon with a color.
private void drawPolygon(com.vividsolutions.jts.geom.Polygon gpoly, Color color, Graphics2D g2d){
java.awt.Polygon poly = (java.awt.Polygon)gpoly;
for(Coordinate co : gpoly.getExteriorRing().getCoordinates() {
poly.addPoint(co.x, co.y);
}
g2d.setColor(col);
g2d.fill(poly);
g2d.setColor(Color.BLACK);
g2d.draw(poly);
}
Sadly java.awt.Polygon does not support Polygons with holes.

Use the Polygon as the basis for an Area (e.g. called polygonShape).
Create an Ellipse2D for the 'hole', then establish an Area for it (ellipseShape).
Use Area.subtract(Area) something like:
Area polygonWithHole = polygonShape.subtract(ellipseShape);

There are some ways to draw shapes or areas that are more complex than a simple polygon (another answer already mentioned Area).
Besides those, you could try to tessellate your final polygon. There are lots of algorithms to do this. For more complex shapes, the algorithms get a bit more complex as well. Basically, you're dividing your final shape into little polygons (usually triangles, but it also can be something else) and then draw those polygons.
You can take a look at your possibilities by searching for "Tessellation Algorithm", there are also some already implemented libraries for Java.

You can use java.awt.geom.Path2D to render a "compound shape" with a hole in it:
If you have java.awt.Shape objects defining the outside & inside edges of the shape, use append(shape, false) to add each shape.
If you have a set of path points for the outside edge and a set of path points for the inside edge, use lineTo() to add the first set of points - creating a closed loop by either ending with the same point you started with, or calling closePath() to automatically close the loop. Then use moveTo() to create a break before adding the inner set of points via more lineTo() calls.
In either case, you must create the path passing Path.WIND_NON_ZERO to the constructor - otherwise the hole won't be left unfilled.
See How to create shape with a hole? for a longer code example.

You could fill the polygon first, and then draw the holes on top, giving the illusion that it filled everything but the holes.

Rendering a triangular face in 3d space

Let's say I have a triangular face in 3d space, and I have the 3d coordinates of each vertex of this triangle, and would also have other information about the triangle(angles, lengths of sides, etc.). In Java, if I have the viewing screen and its information, how can I draw that plane, without using libraries like LWJGL, to that image, assuming I can properly project, accounting for perspective, any 3d point to that 2d image.
Would the best course of action just be to run a loop that draws each point on the plain to a point on the image(i.e. setting the corresponding pixel), which will most likely set the same pixel multiple times? If I'd do this, what would be the best way to identify each point in an oblique triangle, or a triangle that doesn't line up nicely with the axes?
tl;dr: I have a triangular face in 3d space, a "camera" looking at the face, and an image in which I can set each pixel. Using no GL libraries, what's the best way to project and draw that face onto the image?

Projection :
won't detail as you seems to know it
Drawing a line
you can look at Bresenham algorithm if you wanna start with the basics
(hardwared in recent graphics card)
Filling
you can fill between left and right borders of the triangle while you use Bresenham on both (you could use a floodfill algorithm starting ... i don't know, maybe at the projection of the center of the triangle)

Your best bet is to check out the g.fillPolygon() function for Java. It allows you to draw polygons with as many sides as possible and theres also g.drawPolygon() if you don't want it solid. Then you can just do some simple maths for the points. Such as each point is basically it's x and y except if the polygon is further away the points move closer to the center of the polygon and if the polygon is closer they move further away from the center of the polygon.
A second idea could be using some sort of array to store pixels and then researching line drawing algorithms and drawing lines then putting all the line data in another array and using some sort of flood-fill. Then whilst it's in that array you could try and do some weird stuff to the pixels if you wanted textures or something.

Rotating a Sprite in Java

While working on Projectiles I thought that it would be a good idea to rotate the sprite as well, to make it look nicer.
I am currently using a 1-Dimensional Array, and the sprite's width and height can and will vary, so it makes it a bit more difficult for me to figure out on how to do this correctly.
I will be honest and straight out say it: I have absolutely no idea on how to do this. There have been a few searches that I have done to try to find some stuff, and there were some things out there, but the best I found was this:
DreamInCode ~ Rotating a 1-dimensional Array of Pixels
This method works fine, but only for square Sprites. I would also like to apply this for non-square (rectangular) Sprites. How could I set it up so that rectangular sprites can be rotated?
Currently, I'm attempting to make a laser, and it would look much better if it didn't only go along a vertical or horizontal axis.

You need to recalculate the coordinate points of your image (take a look here). You've to do a matrix product of every point of your sprite (x, y) for the rotation matrix, to get the new point in the space x' and y'.
You can assume that the bottom left (or the bottom up, depends on your system coordinate orientation) of your sprite is at (x,y) = (0,0)
And you should recalculate the color too (because if you have a pure red pixel surrounded by blue pixel at (x,y)=(10,5) when you rotate it can move for example to (x, y)=(8.33, 7.1) that it's not a real pixel position because pixel haven't float coordinate. So the pixel at real position (x, y)=(8, 7) will be not anymore pure red, but a red with a small percentage of blue)... but one thing for time.

It's easier than you think: you only have to copy the original rectangular sprites centered into bigger square ones with transparent background. .png files have that option and I think you may use them.

Drawing rectangles for sorting visualizer?

I am attempting to draw rectangles on a canvas that will represent items in a sorting visualizer. I'm really having trouble coming up with an effective way to draw the rectangles proportionately side-by-side on my canvas (centered on my content pane by border layout) to be sorted by various algorithms. I've done some research but haven't really found anything to point me in the right direction. How can they even be moved effectively when the sorting occurs? I suspect each rectangle will be an independent object to be sorted, probably just using the rectangle's height, but how are these objects drawn and moved in relation to one another? Any advice is appreciated. Thanks!

The example provided by MadProgrammer was the most helpful.

How can I create rounded diagonal lines in Java using the ACM library?

I am trying to draw rounded diagonal lines in Java using the ACM library.
A very complicated method would involve drawing a diagonal line, scaling it up to increase its width, drawing an arc on the top of that line with respect to the angles it is rounded.

From the picture you linked to, it looks like you want lines with round end-caps, sometimes called line-joins. I don't know the ACM library too well, but looking at the docs for it, it seems like you could achieve that look by using a GPen with an image that is just a filled-in circle. You could call the setLocation(x,y) and then drawLine(dx, dy) methods on it.

I've never used ACM but looking at the javadoc you might want to consider using shapes rather then lines. So for example, you can draw a rectangle of width using GPolygon then draw circles on the ends using GOval
So something like: draw a polygon around the points [100,0],[0,100],[10,110],[110,10], then draw two circles of size 10 at 0,110 and 110,0. If those shapes are all filled with the same color, they should look like one solid.