How to flip entire awt.Canvas vertically - java

I am sitting with my son, trying to implement a school homework. The task is to write a program that draws X and Y axis and functions, e.g. Sinus or x² into a awt.Canvas. The issue we are struggeling with is that the root, Point(0,0) of the Canvas is designed to be in the upper left corner. The cartesian coordinate system that we have to have, has the origin in the lower left corner. So we tried to apply a AffineTransform and translate in the paint method of the Canvas, which in essence works but has two issues:
1st, for whatever reason the related translation doesn't really moves the origin to the bottom but about 100 pixels to high (see image).
When we put in the below code an additional offset of about 100 pixels with tx.translate(0, -(getHeight()+100)); it looks about right.Same issue seems to be true on the right side. There is also unintended free space. We colored the background of the containing Frame in black and the Canvas in grey to exclude an artefact between these two containers. But doesn't seem to be the case.
2nd, and that concerns us more, is the side effect that all text, when e.g. adding values to the axes will also be fliped, as you see at our debug info in the plotAxes method.
Here is what we have done so far..
public class PlotterView extends Canvas {
protected int MINWIDTH = 500;
protected int MINHEIGHT = 400;
Point[][] lines;
public PlotterView() {
Dimension dim = new Dimension(MINWIDTH, MINHEIGHT);
setPreferredSize(dim);
setBackground(Color.LIGHT_GRAY);
}
protected void plotAxes(Graphics2D g) {
Color defaultColor = g.getColor(); // save to restore defaults in the end
int originX = 5; // x origin of both axes - shift right
int originY = 5; // y origin of both axis - shift up
// Debug info to compare
g.setColor(Color.BLACK);
g.drawString("X: " + originX + "; Y: " + originY, originX, originY);
// X-Axis
g.setColor(Color.RED);
g.drawLine(originX, originY, MINWIDTH-20, originY);
g.drawLine(MINWIDTH-20, originY, MINWIDTH-30, originY-5);
g.drawLine(MINWIDTH-20, originY, MINWIDTH-30, originY+5);
// Y-Axis
g.setColor(Color.BLUE);
g.drawLine(originX, originY, originX, MINHEIGHT-20);
g.drawLine(originX, MINHEIGHT-20, originX-5, MINHEIGHT-30);
g.drawLine(originX, MINHEIGHT-20, originX+5, MINHEIGHT-30);
// Restore defaults
g.setColor(defaultColor);
}
public void paint(Graphics g) {
super.paint(g);
Graphics2D g2 = (Graphics2D) g;
AffineTransform tx = AffineTransform.getScaleInstance(1, -1);
tx.translate(0, -getHeight());
g2.setTransform(tx);
plotAxes(g2);
}
}
One alternative would be to implement a method that "adjusts" every x-value from upper left to lower left, but that feels like a kind of botch job.
How to solve this right? Thank you in advance

Thank you for the feedback. I figured out that issue number 1 is born by using the AffineTransform. If I apply the scale and translate on the g2 directly the issue disappears.
Issue number 2 is a conflict of interest. We couldn't manage to find and apply the "three magic lines of code" (or whatever number would be required) to from thereon programm in a cartesian coordinate system. Instead we are converting all y-values into this top-level-origin coordinate system. Makes the code hard to read, but with the help debugging we managed.

Related

Issues with coordinates

I'm working on something that involves clicking specific points on a buffered image in a JPanel. I had issues with this earlier in the project (affine transform translation not working properly), but nothing I found fixed it so I decided I would come back to it later.
I'm not entirely sure how to trouble shoot it since I'm a novice, but I think it's reading my y coordinates too low. I made a mouse input listener that tracks the number of times the user has clicked and gets the mouse pointer's location for functions I haven't made yet. For testing I have it output the coordinates and number of clicks then make a circle centered where the mouse clicks.
#Override
public void mouseClicked(MouseEvent e) {
Point mouseCursor = MouseInfo.getPointerInfo().getLocation();
panel.drawCenteredCircle(mouseCursor.getX(), mouseCursor.getY(), 100);
System.out.println(String.valueOf(mouseCursor));
System.out.println(String.valueOf(clickCount));
clickCount++;
}
Here is drawCenteredCircle in my custom panel class:
public void drawCenteredCircle(double x, double y, int r) {
imgG2 = image.createGraphics();
imgG2.setPaint(Color.RED);
x = (x-r/2.0);
y = (y-r/2.0);
imgG2.fillOval((int)Math.round(x), (int)Math.round(y), r, r);
this.repaint();
imgG2.dispose();
}
I tried taking a screenshot to show what happens, but the circle properly centers on the x coordinate, but not the y coordinate. Instead it draws the circle with the pointer at the top center edge.
I overrided the paintComponent of my JPanel to implement a zoom feature:
#Override
protected void paintComponent(Graphics g) {
//Implimenting zoom
super.paintComponent(g);
Graphics2D g2 = (Graphics2D)g.create();
g2.setRenderingHint(RenderingHints.KEY_INTERPOLATION, RenderingHints.VALUE_INTERPOLATION_BICUBIC);
/*Supposed to counter the movement from the scale, not working properly
int imageWidth = image.getWidth();
int imageHeight = image.getHeight();
double x = (w - scale * imageWidth)/2;
double y = (h - scale * imageHeight)/2;*/
AffineTransform at = new AffineTransform()/*.getTranslateInstance(x, y) */;
at.scale(scale, scale);
g2.drawRenderedImage(image, at);
//g2.dispose(); I was told to put this, but I'm not sure if it's necessary or what it does entirely
}
My confused notes are because I got this code from an example someone made and, as I said earlier, the affine translation wasn't working (I took the actual translation out). They're irrelevant to the question.
The reason I put this is because I initially had code that was meant to fit the image to the screen/frame depending if it was fullscreen or not:
int x = image.getWidth();
int y = image.getHeight();
double frameW = frame.getBounds().getWidth();
double frameH = frame.getBounds().getHeight();
//Rectangle winSize = GraphicsEnvironment.getLocalGraphicsEnvironment().getMaximumWindowBounds();
double screenW = Toolkit.getDefaultToolkit().getScreenSize().getWidth();
double screenH = Toolkit.getDefaultToolkit().getScreenSize().getHeight();
if (!isFullScreen) {
if (x/y > frameW/frameH) {
scale = frameW/x;
} else {
scale = frameH/y;
}
} else {
if (x/y > screenW/screenH) {
scale = screenW/x;
} else {
scale = screenH/y;
}
}
It uses my zoom function which scales the image with the double "scale." I noticed that when I zoomed in or out, it would change where the dots would appear relative to the pointer. It wasn't until I removed the code for the image to start fitted to the window and had it start at 100% that I received the result of the pointer being at the top center of the circle.
I also tried removing the part that's supposed to center the circle and the result was the pointer being on the left side and having a gap between it and the top of the circle.
Sorry if this is too much stuff. I'm pretty novice and learned just as much about java (the only coding language I know) working on this project as I knew when I first started it. I'm not sure what information I have that could be helpful in this, so I just threw in everything I thought could help. I appreciate any help, even irrelevant to my question.

Using negative height in g.fillRect()

Hello I am trying to paint a bar graph using g.fillRect() to make each bar.
The bars will start at the grid height, y: 700, and fill upwards to y: 350 for example.
I am unable to set a negative x-height for my bar:
public void paint(Graphics g) {
for (Bar b : this.bars) {
g.fillRect(b.x_location,b.y_location,b.width,b.height * (-1));
}
}
This won't paint the bars.
Fix:
public void paint(Graphics g) {
for (Bar b : this.bars) {
g.fillRect(b.x_location,b.y_location - b.height,b.width,b.height);
}
}
You can't, because of the way the API works, it extends down and to the right. Instead, subtract the distance from the y coordinate and maintain the height as a positive value
From the JavaDocs
Fills the specified rectangle. The left and right edges of the rectangle are at x and x + width - 1. The top and bottom edges are at y and y + height - 1. The resulting rectangle covers an area width pixels wide by height pixels tall. The rectangle is filled using the graphics context's current color.
While not a direct duplicate, this example demonstrates the basic concepts

Move a Rectangle from point to point in a ramp with changing angle

So I have this program to test the possibility of an object to slide down in a ramp given its friction, object mass and ramp angle. However I need to animate the box if the force is positive. Just a simple animation moving the box from that point to the end of the ramp. But I can't. Please help
private void drawTransform(Graphics g, double modifier) {
// redtowhite = new GradientPaint(0,0,color.RED,100, 0,color.WHITE);
Rectangle rect = new Rectangle(130,350, 350, 15);
Rectangle box = new Rectangle((int) (rect.getX()+300), 300, 50, 50);
AffineTransform at = new AffineTransform();
at.rotate(-Math.toRadians(modifier), rect.getX(), rect.getY() + rect.height);
// Transform the shape and draw it to screen
Graphics2D g2d = (Graphics2D) g;
g2d.setColor(Color.DARK_GRAY);
// g2d.fillRect(0, 0, 350, 600);
g2d.fill(at.createTransformedShape(rect));
g2d.draw(at.createTransformedShape(box));
}
Screenshot:
If all you want to do is move the box, this can be done by simply updating it's X position. You should be able to manipulate the rectangle's X position directly using something like "box.x++". Alternatively you could create a variable and reference that to provide the initial X co-ordinate, then updating that variable will "move" the box. One issue is this will only move the box along the X axis, hence you will also need some kind of constant downward force acting as gravity. This is easy to achieve, just minus the box's Y position value when it is not colliding with the ground, or your ramp.
Another approach is velocity based movement using vectors, however you mentioned that the animation should be simple. If you do want a smoother animation velocity based movement will provide this but you will need to perform a little research first.

Make oval/rectangle using float/double values

I want to draw a figure using float or double values, to be precise.
I use:
g.drawOval(0, 0, 10, 10);
to draw a circle, but I only can use integer values.
Is there any statement that use float/double values that do the same?
Here is a picture: Problem
The circles have to be centered, and I can't. Any solution?
Code:
import java.awt.Color;
import java.awt.Graphics;
import java.util.Random;
import javax.swing.JPanel;
public class Bulls_EYE extends JPanel
{
int red, green, blue;
int height, width;
int heightOval = 475, widthOval = 475;
Random rValue = new Random();
public void paint (Graphics g)
{
super.paint(g);
for (int idx = 0; idx < 100; idx++)
{
g.setColor(new Color(red = 1 + rValue.nextInt(255), green = 1 + rValue.nextInt(255), blue = 1 + rValue.nextInt(255)));
g.fillOval(width+2*idx, height+2*idx, widthOval-5*idx, heightOval-5*idx);
}
}
}
I think it's an interesting question but needs more context. Drawing primitives are usually expressed in pixel coordinates so fractions of a pixel do not make much sense.
If you want precision like a CAD application note that what is displayed on the screen is only an approximation of the underlying model due to the limitations of the display.
You can represent your models precisely in memory (with limitations in floating point representation) and draw the approximation on the screen.
Update
Based on your last update:
We know from the JavaDoc that fillOval takes as parameters (x, y, w, h) where x, y are the upper left coordinates, and w, h are the width and height.
If for each concentric circle you move the upper left coordinates inward, in this case by 2 px, to keep them centered, you must also reduce the width and height by twice that amount. Change the following line:
g.fillOval(width+2*idx, height+2*idx, widthOval-5*idx, heightOval-5*idx);
To
int dx, dy, dw, dh;
dx = 2*idx;
dy = 2*idx;
dw = 2*dx; // note this is 4*idx not 5*idx like you have currently
dh = 2*dy;
g.fillOval(width+dx, height+dy, widthOval-dw, heightOval-dh);
Note that your width and height variables being used in the first and second parameters really doesn't have anything to do with width and height but instead are providing a beginning offset from the origin where the oval is drawn.
There is no reason you should do this, because when drawing an oval with the given coordinates, they are referred to pixels on the screen. Since you can't draw between pixels, 1 is the smallest unit you can use. If you want to round the values before drawing, you can use
g.drawOval(Math.round(a),Math.round(b),Math.round(x),Math.round(y)
which will round the float a, b, x and y before drawing the oval. The only reason I can see is that you calculate the coordinates and the result is a float, then you need to round it like above.
You can use the Arc2D class for drawing circles with float/double precision, since it is a Shape and the Graphics2D class can draw shapes.
#Override
protected void paintComponent(Graphics g) {
Graphics2D g2d = (Graphics2D) g;
Shape circle = new Arc2D.Double(
// Same values as used in the fillOval function,
// but with double precision.
x, y, width, height,
// Draw a full circle (yes, in degrees).
0, 360,
// Connect the endpoint with the startpoint.
Arc2D.CORD
);
// Paint the circle.
g2d.fill(circle);
}
In a similar way, you can draw rectangles by using the Rectangle2D class.
Also, please use the paintComponent function instead of the paint function, as explained here.

Some help on a Java program to draw a rainbow

I'll be candid about this; it is a homework assignment, but can someone guide me in the right direction and explain to me how some parts of the code are supposed to work? The directions are below the code and the questions.
This is my code so far:
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Container;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class Rainbow extends JPanel
{
// Declare skyColor:
private final Color skyColor = Color.CYAN;
public Rainbow()
{
setBackground(skyColor);
}
// Draws the rainbow.
public void paintComponent(Graphics g)
{
super.paintComponent(g);
int width = getWidth();
int height = getHeight();
// Declare and initialize local int variables xCenter, yCenter
// that represent the center of the rainbow rings:
int xCenter = width/2;
int yCenter = (height * 3) /4;
// Declare and initialize the radius of the large semicircle:
int largeRadius = width/4;
g.setColor(Color.RED);
// Draw the large semicircle:
g.fillArc(xCenter,yCenter,largeRadius,height,0,180);
// Declare and initialize the radii of the small and medium
// semicircles and draw them:
int smallRadius = height/4;
g.setColor(Color.MAGENTA);
g.fillArc(xCenter,yCenter,width,height,0,180);
int mediumRadius = (int) Math.sqrt(smallRadius * largeRadius);
g.setColor(Color.GREEN);
g.fillArc(xCenter,yCenter,width,height,0,180);
// Calculate the radius of the innermost (sky-color) semicircle
// so that the width of the middle (green) ring is the
// arithmetic mean of the widths of the red and magenta rings:
// Draw the sky-color semicircle:
g.fillArc(xCenter,yCenter,width,height,0,180);
}
public static void main(String[] args)
{
JFrame w = new JFrame("Rainbow");
w.setBounds(300, 300, 300, 200);
w.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
Container c = w.getContentPane();
c.add(new Rainbow());
w.setVisible(true);
}
}
My questions: How exactly does fillArc work; I understand what goes in the parameter, but what must one do so each arc differs from one another?
How does one set one color for each arc? I tried doing so, and I ended up with the color listed closest the end showing up and overriding the others.
I'll probably have more as a I continue to code.
These were the directions:
![enter image description here][1]
The “rainbow” is made of four overlapping semicircles. The outer ring is red (Color.RED), the middle one is green (Color.GREEN), and the inner ring has the magenta color (Color.MAGENTA). The innermost semicircle has the same color as the background.
Follow the instructions below and fill in the blanks in Rainbow.java.
Start the Rainbow project.
Add a complete comment header with your name before the class declaration at the top of the file.
Add to the Rainbow class a declaration of a private final field skyColor of the type Color, initialized to Color.CYAN (the color of the sky). In Rainbow’s constructor, set the window’s background to skyColor rather than Color.WHITE.
In the paint method, declare local integer variables xCenter and yCenter that represent the coordinates of the center of the rings. Initialize them to 1/2 width and 3/4 height (down) of the content pane, respectively. (Recall that the origin of graphics coordinates in Java is at the upper left corner of the content pane with the y-axis pointing down.) Do not plug in fixed numbers from the window’s dimensions.
Declare a local variable largeRadius that represents the radius of the largest (red) semicircle and initialize it to 1/4 of width.
A method call g.fillArc(x, y, size, size, from, degrees) (with all integer arguments) draws a sector of a circle. x and y are the coordinates of the upper left corner of the rectangle (in this case a square) into which the oval is (logically) inscribed; size is the side of the square (and the diameter of the circle); from is the starting point of the arc in degrees (with 0 at the easternmost point of the horizontal diameter), and degrees (a positive number) is the measure of the arc, going counterclockwise. Add a statement to the paint method to draw the largest (red) semicircle. Test your program.
Add statements to display the medium (green) and small (magenta) semicircles. The radius of the magenta semicircle should be 1/4 of height. The radius of the green one should be the geometric mean (the square root of the product) of the radius of the red semicircle and the radius of the magenta semicircle, rounded to the nearest integer. (A call to Math.sqrt(x) returns the value of square root of x, a double.) Retest your program.
Add statements to display the innermost semicircle of the background (“sky”) color to complete the rainbow. Use the skyColor constant for this semicircle’s color. Choose the radius of the sky-color semicircle in such a way that the width of the middle (green) ring is the arithmetic mean of the widths of the red and magenta rings.
Test your program.
Submit your completed program and run output. Your run output (the rainbow picture) can be included by capturing the screen output (Alt-PrintScrn), pasting it into a graphics program (such as MS Paint) and then saving the image to your Eclipse project directory.
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Container;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class Rainbow extends JPanel
{
//Declare skyColor:
private final Color skyColor = Color.CYAN;
public Rainbow()
{
setBackground(skyColor);
}
// Draws the rainbow.
public void paintComponent(Graphics g)
{
super.paintComponent(g);
int width = getWidth();
int height = getHeight();
// Declare and initialize local int variables xCenter, yCenter
// that represent the center of the rainbow rings:
int xCenter = width/2;
int yCenter = (height * 3) /4;
// Declare and initialize the radius of the large semicircle:
int largeRadius = width/4;
g.setColor(Color.RED);
// Draw the large semicircle:
g.fillArc(xCenter - largeRadius,yCenter - largeRadius ,largeRadius,largeRadius,0,180);
// Declare and initialize the radii of the small and medium
//semicircles and draw them:
int smallRadius = height/4;
int mediumRadius = (int) Math.sqrt(smallRadius * largeRadius);
g.setColor(Color.GREEN);
g.fillArc(xCenter-(largeRadius+mediumRadius)/2,yCenter- (largeRadius+mediumRadius)/2,mediumRadius,mediumRadius,0,180);
g.setColor(Color.MAGENTA);
g.fillArc(xCenter-(largeRadius+smallRadius)/2,yCenter-(largeRadius+smallRadius)/2,smallRadius,smallRadius,0,180);
// Calculate the radius of the innermost (sky-color) semicircle
// so that the width of the middle (green) ring is the
// arithmetic mean of the widths of the red and magenta rings:
int skyRadius = (int)((2 * Math.sqrt(smallRadius * largeRadius)) - width/4);
// Draw the sky-color semicircle:
g.setColor(skyColor);
g.fillArc(xCenter-skyRadius,yCenter-skyRadius,skyRadius,skyRadius,0,180);
}
public static void main(String[] args)
{
JFrame w = new JFrame("Rainbow");
w.setBounds(300, 300, 300, 200);
w.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
Container c = w.getContentPane();
c.add(new Rainbow());
w.setVisible(true);
}
}
fillArc() fills in a section of the circle based upon the parameters you gave it. For example your first arc.
You're drawing the fill arc, which in this case is a semi-circle, of the color red.
//Set the arc color
g.setColor(Color.RED);
// Draw the large semicircle:
g.fillArc(xCenter,yCenter,largeRadius,height,0,180);
There's our fillArc. That doesn't look anything like a rainbow. In order to get the rainbow shape, we have to draw a smaller arc inside of it. In your case the next one is green. So we do fillArc again after setting the color to green. But we shrunk the radius a little bit so the green doesn't cover the entire red section.
Keep in mind when we draw, we're drawing on top, so if you drew the green on first it would be covered by the red one.
Then we draw another arc inside this once more, but make this one the color of the sky (white in this case). This creates the final rainbow shape. So we do fillArc again, but with a slightly smaller radius and the color white.
And there, we drew a rainbow.
To center this beautiful creation, we have to understand a few things about the fillArc function.
The parameters are:
public abstract void fillArc(int x,
int y,
int width,
int height,
int startAngle,
int arcAngle)
int x and int y represent the coordinates for the upper left hand corner of the arc that you are drawing. The reason your code isn't centering is because of how you're drawing the arc.
g.fillArc(xCenter - largeRadius,yCenter - largeRadius,largeRadius,largeRadius,0,180);
g.fillArc(xCenter-(largeRadius+mediumRadius)/2,yCenter-(largeRadius+mediumRadius)/2,mediumRadius,mediumRadius,0,180);
g.fillArc(xCenter-(largeRadius+smallRadius)/2,yCenter-(largeRadius+smallRadius)/2,smallRadius,smallRadius,0,180);
I took out a few of the excess stuff. You see how you're subtracting the (largeRadius+smallRadius)/2 and (largeRadius+mediumRadius)/2? This is shifting the rainbow to make it off center. What you should have is instead:
g.fillArc(xCenter - largeRadius/2,yCenter - largeRadius,largeRadius,largeRadius,0,180);
g.fillArc(xCenter-(mediumRadius)/2,yCenter-(largeRadius+mediumRadius)/2,mediumRadius,mediumRadius,0,180);
g.fillArc(xCenter-(smallRadius)/2,yCenter-(largeRadius+smallRadius)/2,smallRadius,smallRadius,0,180);
This will properly center the rainbow. Here's why.
That's the point where they will start the drawing the arc from. If you want to center the entire rainbow, you'd shift it over by half of it's entire width. So if you want to center the red arc, you'd do
xCenter - (largeRadius/2)
As this is setting the x start to the left by half. You wouldn't include largeRadius in the other arcs, as you're centering them around this point. Thus you'd want to shift them over by half of their individual widths, which is why their x positions are
xCenter-(mediumRadius)/2
xCenter-(smallRadius)/2
Centering on the Y-axis works differently. You have to consider that the height of the rainbow overall is 1/4 the largeRadius. Your code uses yCenter = 3/4 * height, so that changes it a bit.
This is my solution
g.fillArc(xCenter - largeRadius/2,yCenter - largeRadius/2 + largeRadius/4 -height/4,largeRadius,largeRadius,0,180);
g.fillArc(xCenter-(mediumRadius)/2,yCenter-(mediumRadius)/2 + largeRadius/4 -height/4,mediumRadius,mediumRadius,0,180);
g.fillArc(xCenter-(smallRadius)/2,yCenter-(smallRadius)/2 + largeRadius/4 -height/4,smallRadius,smallRadius,0,180);
Let's take a look. I subtracted the largeRadius/2 (and respective radiuses) for the same principle as in x. But then I added largeRadius/4 because we have to shift the entire rainbow down. This is because subtracting the respective radius/2 only centers the rainbow as if it were an entire circle, not semi-circles.
Adding largeRadius/4 shifts the rainbow down by overall half of it's height, centering it correctly for a semi-circle. Finally, subtracting height/4 makes changes the yCenter to height/2, since 3/4 * height is a requirement in your assignment.
Sorry about all the problems in the comments, hope this cleared it up.
I've modified part of your code so you could get an idea. Remember that your xCenter and yCenter represent the center of your circle, not the coordinates you need to use in the fillArc method. The instructions you provided explain it pretty well. You can get an idea from what I did here and figure the rest by yourself.
// First declare and initialize all radiuses
int largeRadius = width/4;
int smallRadius = height/4;
int mediumRadius = (int) Math.sqrt(smallRadius * largeRadius);
//Then draw each arc in descending order from the largest one
g.setColor(Color.RED);
g.fillArc(xCenter-largeRadius,yCenter-largeRadius,largeRadius,largeRadius,0,180);
g.setColor(Color.GREEN);
g.fillArc(xCenter-(largeRadius+mediumRadius)/2,yCenter-(largeRadius+mediumRadius)/2,mediumRadius,mediumRadius,0,180);
g.setColor(Color.MAGENTA);
g.fillArc(xCenter-(largeRadius+smallRadius)/2,yCenter-(largeRadius+smallRadius)/2,smallRadius,smallRadius,0,180);
// Calculate the radius of the innermost (sky-color) semicircle
For you skyRadius consider:
Red width = large radius - medium radius
green width = medium - small
magenta width = small radius - skyradius
if I did the math rightyou get: skyRadius = smallRadius - 2*(mediumRadius-smallRadius)+largeRadius-mediumRadius
int skRadius=smallRadius-2*(mediumRadius-smallRadius)+largeRadius-mediumRadius;
g.setColor(skyColor);
g.fillArc(xCenter-(largeRadius+skRadius)/2,yCenter-(largeRadius+skRadius)/2,skRadius,skRadius,0,180);
A much simpler equation for skyRadius is:
int skyRadius = largeRadius - 3 * mediumRadius + 3 * smallRadius;

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