Drawing polar curve Lemiscate bug - c#

I´m trying to draw a lemiscate. My code isn't drawing the curve correctly. Why does the line start or end at the point 0,0 (left corner)?
private void drawLemiscate(Graphics g, int a, int Sx,int Sy)
{
int x, y;
Point[] p = new Point[720];
for (int phi = 0; phi < 720; phi++)
{
int r = (int)(a * Math.Cos(2 * degreeToRadians(phi)));
if (r > 0)
continue;
x = (int)Math.Round((r * Math.Sin(degreeToRadians(phi)) + Sx));
y = (int)Math.Round((r * Math.Cos(degreeToRadians(phi)) + Sy));
p[phi] = new Point(x, y);
}
Pen pen = new Pen(Color.Red, 1);
g.DrawLines(pen, p);
canvas.Invalidate();
}
private double degreeToRadians(double angle)
{
return Math.PI * angle / 180.0;
}

You should investigate which element of p is (0, 0). You can use the debugger to inspect it or use a loop to look for it and print out which index(es) have (0, 0).
Hint: consider what effect if (r > 0) continue; has on your output.

Related

Drawing points along path spirally

Well, I'm trying to optimize what I did here (Smoothing noises with different amplitudes (Part 2)).
By this reason, I did a new implementation from scratch (https://youtu.be/o7pVEXhh3TI) to draw the path:
private void Start()
{
Polygon pol = File.ReadAllText(PolyPath).Deserialize<Polygon>();
// Create tex object
var list = pol.Vertices.AsEnumerable();
tex = list.CreateTextureObject(pol.Position, offset);
exampleTexture = new Texture2D(tex.Width, tex.Height);
exampleTexture.SetPixels32(new Color32[tex.Width * tex.Height]);
exampleTexture.Apply();
vertices = pol.Vertices.Select(v => (v - pol.Position) + offset).Clone().ToList();
_ss = new List<Segment>(pol.Segments.Select(s => new Segment((s.start + pol.Center - pol.Position) + offset, (s.end + pol.Center - pol.Position) + offset)));
foreach (Segment curSeg in _ss)
for (int i = -effectDistance; i < effectDistance; ++i)
{
Vector2 perp = Vector2.Perpendicular(((Vector2)curSeg.start - (Vector2)curSeg.end)).normalized;
segments.Add((Vector2)curSeg.start + perp * i);
F.DrawLine((Vector2)curSeg.start + perp * i, (Vector2)curSeg.end + perp * i, (x, y) => layers.Add(new Point(x, y)));
}
Debug.Log("Layer Count: " + layers.Count);
drawPath = true;
}
private void OnGUI()
{
if (exampleTexture == null)
return;
GUI.DrawTexture(new Rect((Screen.width - tex.Width) / 2, (Screen.height - tex.Height) / 2, tex.Width, tex.Height), exampleTexture);
if (drawPath)
{
{
Point? cur = layers.Count > 0 ? (Point?)layers.First() : null;
if (cur.HasValue)
{
exampleTexture.SetPixel(cur.Value.x, cur.Value.y, new Color32(170, 0, 0, 255));
exampleTexture.Apply();
layers.Remove(cur.Value);
}
}
{
Point? cur = segments.Count > 0 ? (Point?)segments.First() : null;
if (cur.HasValue)
{
exampleTexture.SetPixel(cur.Value.x, cur.Value.y, new Color32(0, 170, 0, 255));
exampleTexture.Apply();
segments.Remove(cur.Value);
}
}
{
Point? cur = vertices.Count > 0 ? (Point?)vertices.First() : null;
//Debug.Log(cur);
if (cur.HasValue)
{
exampleTexture.SetPixel(cur.Value.x, cur.Value.y, new Color32(255, 128, 0, 255));
exampleTexture.Apply();
vertices.Remove(cur.Value);
}
}
if (vertices.Count == 0 && segments.Count == 0 && layers.Count == 0)
drawPath = false;
}
}
This is what DrawLines actually do:
public static class F
{
public static void DrawLine(Point p1, Point p2, Action<int, int> action)
{
DrawLine(p1.x, p1.y, p2.x, p2.y, action);
}
public static void DrawLine(int x0, int y0, int x1, int y1, Action<int, int> action)
{
int sx = 0,
sy = 0;
int dx = Mathf.Abs(x1 - x0),
dy = Mathf.Abs(y1 - y0);
if (x0 < x1) { sx = 1; } else { sx = -1; }
if (y0 < y1) { sy = 1; } else { sy = -1; }
int err = dx - dy,
e2 = 0;
while (true)
{
action?.Invoke(x0, y0);
if ((x0 == x1) && (y0 == y1))
break;
e2 = 2 * err;
if (e2 > -dy)
{
err = err - dy;
x0 = x0 + sx;
}
if (e2 < dx)
{
err = err + dx;
y0 = y0 + sy;
}
}
}
}
This is an implemenentation of Bresenham algorithm.
This implementation is better because I have lowered iterations from 280k to 6k, but there is an issue as you can see this is innacurate...
The way this works first is getting the perpendicular of each segment on the shape (green pixels) and then drawing lines between the start and the end point of that segment. Segmenents are obtained using Ramer-Douglas-Peucker algorithm.
So I was thinking on draw the "orange" path spirally. I don't know how to explain this, basically, obtaining the same path but, with an scale (Translating/transforming? list of points from its center with an offset/distance) but I think I will have the same innacuracy.
Any guide will be appreciated. What algorithm could I use to draw the path with "layers"?
Following some of the information here, you might be able to use "inward/outward polygon offsetting" (aka "polygon buffering") to get the result you are interested in.
A tool such as Clipper can help.
Once you have a way to outwardly offset your shape, do the following:
First, draw the outer shape (black region below), then offset the inner shape outwards as far as you need it to go, and draw it on top of the outer shape (brown region below) using an appropriate noise/color scheme:
Then, apply a smaller offset, then draw that shape on top using a different noise/colorscheme (orange region below).
Repeat until you have as many gradients as you need:
Finally, draw the inner shape without any offsetting with its noise/color scheme:

Draw a curve of the Cycloid

Good time of day. It is necessary to draw a graph of the cycloids, the radius is specified by the user. Managed to paint only half of the period, I do not understand what it is.
Code'm applying.
My function:
return r * Math.Acos((r - y) / r) - Math.Sqrt(2 * r * y - Math.Pow(y, 2));
And my Main part:
GraphPane pane = zedGraph.GraphPane;
pane.CurveList.Clear();
PointPairList list = new PointPairList();
double r = 20;
double xmax = 50;
for (double y = 0; y < xmax; y+=0.5)
{
list.Add(CountIt(y, r), y);
}
LineItem myCurve = pane.AddCurve("Cycloid", list, Color.Red, SymbolType.None);
zedGraph.AxisChange();
zedGraph.Invalidate();
Apparently it is necessary to consider the situation when y>2r, or that should be several possible x? I do not understand how to get out of the situation.
It is simpler to use parametric equations (with t=0..2*Pi for one period):
x = r * (t - sin(t))
y = r * (1 - cos(t))
If you want to continue using Cartesian equation x(y) - change limit for y to correct value 2 * r and mirror the second part like this:
for (double y = 0; y < 2 * r; y+=0.5)
{
list.Add(CountIt(y, r), y);
}
for (double y = 2 * r; y >= 0; y-=0.5)
{
list.Add(2 * Pi * r - CountIt(y, r), y);
}
If you need to draw few periods, limiting xmax:
p = 0;
while true do
{
for (double y = 0; y < 2 * r; y+=0.5)
{ x = 2 * Pi * r * p + CountIt(y, r);
if (x > xmax)
break;
list.Add(x, y);
}
for (double y = 2 * r; y >= 0; y-=0.5)
{
x = 2 * Pi * r * (p + 1) - CountIt(y, r);
if (x > xmax)
break;
list.Add(x, y);
}
p++;
}

Drawing y = sin(θ) * cos(θ) in C# with a Pen

I want to draw sin(θ)*cos(θ), but it doesn't work.
I can draw sin or cos,
but I want to draw sin(θ)*cos(θ) together.
Here is my code
private void button1_Click(object sender, EventArgs e)
{
Graphics drw = this.CreateGraphics();
Pen pen = new Pen(Brushes.Black, 7.0f);
float x1 = 0;
float y1 = 0;
float xoy = 200;
float ef = 20;
for (double i=0;i<40;i+=1)
{
double radi = (float)(i * 180 / Math.PI);
float temp = (float)Math.Cos(radi)*(float)Math.Sin(radi);
drw.DrawLine(pen, x1 * ef, y1 * ef + xoy, ef * (float)i, temp * ef + xoy);
x1 = (float)i;
y1 = temp;
}
}
And I want this result:
You may find it easier to look at the corresponding Parametric Equations.
private void Form1_Paint(object sender, PaintEventArgs e)
{
var g = e.Graphics;
double pi = Math.PI;
int n = 100;
var t = Enumerable.Range(0, n).Select(p => p * 2 * pi / n).ToArray();
var x = t.Select(p => Math.Sin(2 * p) * Math.Cos(p)).ToArray();
var y = t.Select(p => Math.Sin(2 * p) * Math.Sin(p)).ToArray();
Pen pen = new Pen(Brushes.Black, 3);
int scale = 100;
int shift = 100;
for (int i = 0; i < n - 1; i++)
{
g.DrawLine(pen, scale*(float)x[i] + shift,
scale*(float)y[i] + shift,
scale*(float)x[i + 1] + shift,
scale*(float)y[i + 1] + shift);
}
}
Actually, the real function you are looking for is a little bit different... see an example here. Looking at this article about polar flowers, I'm sure it will get pointed to the right direction, and it also contains a full working source code.
Just an example, supposing you use a panel in your form on which to draw the polar flower:
panel.OnPaint += Panel_Paint;
private void Panel_Paint(Object sender, PaintEventArgs e)
{
Double scale = ((Panel)sender).Width / 2.0d;
Double repetitions = Math.Round(scale, 0);
Double basis = (2.0d * Math.PI) / scale;
Double petals = 2.0d;
using (Graphics g = e.Graphics)
{
using (Pen pen = new Pen(Brushes.Red, 2.0f))
{
for (Double i = 0.0f; i < (repetitions - 1); ++i)
{
Double t0 = i*basis;
Double t1 = (i + 1)*basis;
Double x0 = Math.Sin(petals * t0) * Math.Cos(t0);
Double x1 = Math.Sin(petals * t1) * Math.Cos(t1);
Double y0 = Math.Sin(petals * t0) * Math.Sin(t0);
Double y1 = Math.Sin(petals * t1) * Math.Sin(t1);
g.DrawLine
(
pen,
(Single) ((scale*x0) + scale),
(Single) ((scale*y0) + scale),
(Single) ((scale*x1) + scale),
(Single) ((scale*y1) + scale)
);
}
}
}
}
The basic formulation states that if the petals variable value is:
even, then it represents half the amount of petals of the polar flower
odd, then it represents the amount of petals of the polar flower
so if you define Double petals = 2.0d;, you will obtain 4 petals... and if you define Double petals = 5.0d;, you will obtain 5 petals.

Traverse Pixels in a circle from the center

I need an algorithm like Bresenham's circle algorithm, but with some modifications.
The algorithm must visit all pixels in the radius (so essentially a fill).
The algorithm must start from the center of the circle
It must visit all points that would normally be visited (no holes)
It must visit each point in the circle exactly once
One technique I came up with would first determine all pixel coordinates inside the circle by just going through the rectangle of the circle and checking with Math.Sqrt if it is inside the circle.
Then it would order the pixels by distance and then visit each of them.
That would be exactly what I want, with the exception of being fast.
So my questions is:
Is there a fast way to do this without fetching,ordering and then visiting each pixel?
Just for clarification I do not actually want to draw onto the image, I only want to traverse them in the described order.
First, we can use fact, that circle can be divided in 8 octants. So we just need to fill single octant and use simple +- coordinate change to get full circle. So if we try to fill only one octant, we need to worry only about 2 directions from center : left and left top. Also, clever use of data structures like priority queue (.NET doesn't have it, so you need to find it somewhere else) and hash map can drastically improve performance.
/// <summary>
/// Make sure it is structure.
/// </summary>
public struct Point
{
public int X { get; set; }
public int Y { get; set; }
public int DistanceSqrt()
{
return X * X + Y * Y;
}
}
/// <summary>
/// Points ordered by distance from center that are on "border" of the circle.
/// </summary>
public static PriorityQueue<Point> _pointsToAdd = new PriorityQueue<Point>();
/// <summary>
/// Set of pixels that were already added, so we don't visit single pixel twice. Could be replaced with 2D array of bools.
/// </summary>
public static HashSet<Point> _addedPoints = new HashSet<Point>();
public static List<Point> FillCircle(int radius)
{
List<Point> points = new List<Point>();
_pointsToAdd.Enqueue(new Point { X = 1, Y = 0 }, 1);
_pointsToAdd.Enqueue(new Point { X = 1, Y = 1 }, 2);
points.Add(new Point {X = 0, Y = 0});
while(true)
{
var point = _pointsToAdd.Dequeue();
_addedPoints.Remove(point);
if (point.X >= radius)
break;
points.Add(new Point() { X = -point.X, Y = point.Y });
points.Add(new Point() { X = point.Y, Y = point.X });
points.Add(new Point() { X = -point.Y, Y = -point.X });
points.Add(new Point() { X = point.X, Y = -point.Y });
// if the pixel is on border of octant, then add it only to even half of octants
bool isBorder = point.Y == 0 || point.X == point.Y;
if(!isBorder)
{
points.Add(new Point() {X = point.X, Y = point.Y});
points.Add(new Point() {X = -point.X, Y = -point.Y});
points.Add(new Point() {X = -point.Y, Y = point.X});
points.Add(new Point() {X = point.Y, Y = -point.X});
}
Point pointToLeft = new Point() {X = point.X + 1, Y = point.Y};
Point pointToLeftTop = new Point() {X = point.X + 1, Y = point.Y + 1};
if(_addedPoints.Add(pointToLeft))
{
// if it is first time adding this point
_pointsToAdd.Enqueue(pointToLeft, pointToLeft.DistanceSqrt());
}
if(_addedPoints.Add(pointToLeftTop))
{
// if it is first time adding this point
_pointsToAdd.Enqueue(pointToLeftTop, pointToLeftTop.DistanceSqrt());
}
}
return points;
}
I will leave the expansion to full list on you. Also make sure borders of the octants don't cause doubling of the points.
Ok, I couldn't handle it and did it myself. Also, to make sure it has properties you desire I did simple test :
var points = FillCircle(50);
bool hasDuplicates = points.Count != points.Distinct().Count();
bool isInOrder = points.Zip(points.Skip(1), (p1, p2) => p1.DistanceSqrt() <= p2.DistanceSqrt()).All(x => x);
I found a solution that satisfies my performance needs.
It's very simple, just a offset array.
static Point[] circleOffsets;
static int[] radiusToMaxIndex;
static void InitCircle(int radius)
{
List<Point> results = new List<Point>((radius * 2) * (radius * 2));
for (int y = -radius; y <= radius; y++)
for (int x = -radius; x <= radius; x++)
results.Add(new Point(x, y));
circleOffsets = results.OrderBy(p =>
{
int dx = p.X;
int dy = p.Y;
return dx * dx + dy * dy;
})
.TakeWhile(p =>
{
int dx = p.X;
int dy = p.Y;
var r = dx * dx + dy * dy;
return r < radius * radius;
})
.ToArray();
radiusToMaxIndex = new int[radius];
for (int r = 0; r < radius; r++)
radiusToMaxIndex[r] = FindLastIndexWithinDistance(circleOffsets, r);
}
static int FindLastIndexWithinDistance(Point[] offsets, int maxR)
{
int lastIndex = 0;
for (int i = 0; i < offsets.Length; i++)
{
var p = offsets[i];
int dx = p.X;
int dy = p.Y;
int r = dx * dx + dy * dy;
if (r > maxR * maxR)
{
return lastIndex + 1;
}
lastIndex = i;
}
return 0;
}
With this code you just get the index where to stop from radiusToMaxIndex, then loop through circleOffsets and visit those pixels.
It will cost lot of memory like this, but you can always change the datatype of the offsets from Point to a custom one with Bytes as members.
This solution is extremely fast, fast enough for my needs. It obviously has the drawback of using some memory, but lets be honest, instantiating a System.Windows.Form uses up more memory than this...
You have already mentioned Bresenhams's circle algorithm. That is a good starting point: You could start with the centre pixel and then draw Bresenham circles of increasing size.
The problem is that the Bresenham circle algorithm will miss pixels near the diagonals in a kind of Moiré effect. In another question, I have adopted the Bresenham algorithm for drawing between an inner and outer circle. With that algorithm as base, the strategy of drawing circles in a loop works.
Because the Bresenham algorithm can place pixels only at discrete integer coordinates, the order of visiting pixels will not be strictly in order of increasing distance. But the distance will always be within one pixel of the current circle you are drawing.
An implementation is below. That's in C, but it only uses scalars, so it shouldn't be hard to adapt to C#. The setPixel is what you do to each pixel when iterating.
void xLinePos(int x1, int x2, int y)
{
x1++;
while (x1 <= x2) setPixel(x1++, y);
}
void yLinePos(int x, int y1, int y2)
{
y1++;
while (y1 <= y2) setPixel(x, y1++);
}
void xLineNeg(int x1, int x2, int y)
{
x1--;
while (x1 >= x2) setPixel(x1--, y);
}
void yLineNeg(int x, int y1, int y2)
{
y1--;
while (y1 >= y2) setPixel(x, y1--);
}
void circle2(int xc, int yc, int inner, int outer)
{
int xo = outer;
int xi = inner;
int y = 0;
int erro = 1 - xo;
int erri = 1 - xi;
int patch = 0;
while (xo >= y) {
if (xi < y) {
xi = y;
patch = 1;
}
xLinePos(xc + xi, xc + xo, yc + y);
yLineNeg(xc + y, yc - xi, yc - xo);
xLineNeg(xc - xi, xc - xo, yc - y);
yLinePos(xc - y, yc + xi, yc + xo);
if (y) {
yLinePos(xc + y, yc + xi, yc + xo);
xLinePos(xc + xi, xc + xo, yc - y);
yLineNeg(xc - y, yc - xi, yc - xo);
xLineNeg(xc - xi, xc - xo, yc + y);
}
y++;
if (erro < 0) {
erro += 2 * y + 1;
} else {
xo--;
erro += 2 * (y - xo + 1);
}
if (y > inner) {
xi = y;
} else {
if (erri < 0) {
erri += 2 * y + 1;
} else {
xi--;
erri += 2 * (y - xi + 1);
}
}
}
if (patch) {
y--;
setPixel(xc + y, yc + y);
setPixel(xc + y, yc - y);
setPixel(xc - y, yc - y);
setPixel(xc - y, yc + y);
}
}
/*
* Scan pixels in circle in order of increasing distance
* from centre
*/
void scan(int xc, int yc, int r)
{
int i;
setPixel(xc, yc);
for (i = 0; i < r; i++) {
circle2(xc, yc, i, i + 1);
}
}
This code takes care of not visiting pixels that are in two octants by skipping coincident picels on alterante octants. (Edit: There was still abug in the original code, but it's fixed now by means of the ´patch` variable.)
There's also room for improvement: The inner circle is basically the outer circle of the previous iteration, so there's no point in calculating it twice; you could keep an array of the outer points of the previous circle.
The xLinePos functions are also a bit too complicated. There are never more than two pixels drawn in that function, usually only one.
If the roughness of the search order bothers you, you can run a more exact algorithm once at the beginning of the program, where you calculate a traversing order for all circles up to a reasonable maximum radius. You can then keep that data and use it for iterating all circles with smaller radii.

Defining Regions for Venn Diagram using Graphics Regions

I have created a Venn diagram using simple Graphics functions provided by WinForm in the onPaint event. Here is my code for creating the Venn.
using (Brush brushLeft = new SolidBrush(LeftVennColor))
{
leftvennPath.AddEllipse(leftVenn);
leftOnlyRegion = new Region(leftVenn);
e.Graphics.FillEllipse(brushLeft, leftVenn);
e.Graphics.DrawEllipse(pen, leftVenn);
}
using (Brush brushRight = new SolidBrush(RightVennColor))
{
rightvennPath.AddEllipse(rightVenn);
rightOnlyRegion = new Region(rightVenn);
e.Graphics.FillEllipse(brushRight, rightVenn);
e.Graphics.DrawEllipse(pen, rightVenn);
}
using (GraphicsPath circle_path = new GraphicsPath())
{
circle_path.AddEllipse(leftVenn);
commonRegion.Intersect(circle_path);
}
using (GraphicsPath circle_path = new GraphicsPath())
{
circle_path.AddEllipse(rightVenn);
commonRegion.Intersect(circle_path);
}
The Venn diagram is created, but with this code my common region is the intersection of both left and right ellipses. I want to have two separate regions out of that common area, which is separated by a line. Here is the image for that,
So basically, I need all these four regions separated and clickable ( different colors for each region ).. I use Region.IsVisible(e.location) in the mouse click event to handle the click event. Could someone please help?
Final solution:
cx0, cy0, radius0 center and radius of left circle
cx1, cy1, radius1 center and radius of right circle
The function takes the regions by ref.
private void FindRegions(int cx0, int cx1, int cy0, int cy1, int radius0, int radius1, ref Region rgnLeft, ref Region rgnRight)
{
//Left circle
GraphicsPath gpL = new GraphicsPath();
//Right circle
GraphicsPath gpR = new GraphicsPath();
//The right small region (yellow color)
GraphicsPath gp = new GraphicsPath();
//Points of intersection
PointF pnt1 = new PointF();
PointF pnt2 = new PointF();
Graphics g = this.CreateGraphics();
gpL.AddEllipse(new Rectangle(cx0 - radius0, cy0 - radius0, 2 * radius0, 2 * radius0));
gpR.AddEllipse(new Rectangle(cx1 - radius0, cy1 - radius1, 2 * radius1, 2 * radius1));
g.DrawPath(Pens.Red, gpL);
g.DrawPath(Pens.Blue, gpR);
int numPoints = FindCircleCircleIntersections((single)cx0, (single)cx1, (single)cy0, (single)cy1, (single)radius0, (single)radius1, ref pnt1, ref pnt2);
if (numPoints != 2)
{
//No regions
return;
}
Double theta, fe;
Double dx = (double)pnt1.X - (double)pnt2.X;
Double dy = (double)pnt1.Y - (double)pnt2.Y;
Double dist = Math.Sqrt(dx * dx + dy * dy);
PointF minPoint, maxPoint;
if (pnt2.Y < pnt1.Y)
{
minPoint = pnt2;
maxPoint = pnt1;
}
else
{
minPoint = pnt1;
maxPoint = pnt2;
}
//theta is the angle between the three points pnt1, pnt2 and left center
theta = Math.Acos((dist / 2D) / 100D);
theta = (theta * 180D) / Math.PI;
theta = 90D - theta;
theta *= 2D;
//fe is the starting angle of the point(between pnt1 and pnt2) with
//the smaller y coordinate. The angle is measured from x axis and clockwise
fe = Math.Asin( Math .Abs ( (-(Double)minPoint.Y + (double)cy0) )/ (double)radius0);
fe = (fe * 180D) / Math.PI;
if (minPoint.X > cx0 && minPoint.Y >= cy0)
{
//fe = (90 - fe) + 270;
}
else if (minPoint.X > cx0 && minPoint.Y < cy0)
{
fe = (90D - fe) + 270D;
}
else if (minPoint.X == cx0 && minPoint.Y < cy0)
{
fe = 270D;
}
else
{
fe += 180D;
}
gp.AddArc(new Rectangle(cx0 - radius0, cy0 - radius0, 2 * radius0, 2 * radius0), (float)fe, (float)theta);
gp.AddLine(maxPoint, minPoint);
gp.CloseFigure();
g.DrawPath(Pens.Green, gp);
Region rgnL = new Region(gpL);
Region rgnR = new Region(gpR);
Region rgnInt = new Region(gpL);
Region rgn = new Region(gp); //right small
rgnInt.Intersect(rgnR);
rgnInt.Exclude(rgn); //left small
g.FillRegion(Brushes.DarkGreen, rgnInt);
g.FillRegion(Brushes.DarkGray, rgn);
rgnLeft = rgnInt.Clone();
rgnRight = rgn.Clone();
g.Dispose();
rgnL.Dispose();
rgnR.Dispose();
rgnInt.Dispose();
rgn.Dispose();
gpL.Dispose();
gpR.Dispose();
gp.Dispose();
}
private int FindCircleCircleIntersections(Single cx0, Single cx1, Single cy0, Single cy1, Single radius0, Single radius1,
ref PointF intersection1, ref PointF intersection2)
{
// Find the distance between the centers.
Single dx = cx0 - cx1;
Single dy = cy0 - cy1;
Double dist = Math.Sqrt(dx * dx + dy * dy);
// See how many solutions there are.
if (dist > radius0 + radius1)
{
//No solutions, the circles are too far apart.
intersection1 = new PointF(Single.NaN, Single.NaN);
intersection2 = new PointF(Single.NaN, Single.NaN);
return 0;
}
else if (dist < Math.Abs(radius0 - radius1))
{
// No solutions, one circle contains the other.
intersection1 = new PointF(Single.NaN, Single.NaN);
intersection2 = new PointF(Single.NaN, Single.NaN);
return 0;
}
else if ((dist == 0) && (radius0 == radius1))
{
// No solutions, the circles coincide.
intersection1 = new PointF(Single.NaN, Single.NaN);
intersection2 = new PointF(Single.NaN, Single.NaN);
return 0;
}
else
{
// Find a and h.
Double a = (radius0 * radius0 - radius1 * radius1 + dist * dist) / (2 * dist);
Double h = Math.Sqrt(radius0 * radius0 - a * a);
// Find P2.
Double cx2 = cx0 + a * (cx1 - cx0) / dist;
Double cy2 = cy0 + a * (cy1 - cy0) / dist;
// Get the points P3.
intersection1 = new PointF( (Single)(cx2 + h * (cy1 - cy0) / dist), (Single)(cy2 - h * (cx1 - cx0) / dist));
intersection2 = new PointF( (Single)(cx2 - h * (cy1 - cy0) / dist), (Single)(cy2 + h * (cx1 - cx0) / dist));
// See if we have 1 or 2 solutions.
if (dist == radius0 + radius1) return 1;
return 2;
}
}
EDIT
Region has only a Fill method and no Draw one. So you cant do it with regions. GraphicPath
however HAS both Fill and Draw.
You said that you need to validate if a point is inside the region BUT you can do the same with GraphicPath
myGraphicPath.IsVisible();
So, dont use regions but paths. It is better for another reason. GraphicPath can draw AntiAlias but regions dont. Set
g.SmoothingMode = SmoothingMode.AntiAlias;
To enable AntiAlias. All goodies with paths!
Change the function name from FindRegions to FindPaths and send paths as refference:
private void FindPaths(int cx0, int cx1, int cy0, int cy1, int radius0, int radius1, ref GraphicsPath gpLeft, ref GraphicsPath gpRight)
The code is exactly the same, but add in the and:
private void FindPaths(int cx0, int cx1, int cy0, int cy1, int radius0, int radius1, ref GraphicsPath gpLeft, ref GraphicsPath gpRight)
{
...
...
//Above code exactly the same
//replace these
//rgnLeft = rgnInt.Clone();
//rgnRight = rgn.Clone();
//with these
GraphicsPath gpLeftSmall = (GraphicsPath)gp.Clone();
Matrix matrix = new Matrix();
PointF pntf = new PointF();
pntf.X = (float)(Math.Min((double)pnt1.X, (double)pnt2.X) + Math.Abs((double)(pnt1.X - pnt2.X) / 2D));
pntf.Y = (float)(Math.Min((double)pnt1.Y, (double)pnt2.Y) + Math.Abs((double)(pnt1.Y - pnt2.Y) / 2D));
matrix.RotateAt(180, pntf);
gpLeftSmall.Transform(matrix);
g.DrawPath(Pens.Black, gpLeftSmall); //If you want to draw it
//passed by refference
gpLeft = gpLeftSmall.Clone();
gpRight = gp.Clone();
g.Dispose();
rgnL.Dispose();
rgnR.Dispose();
rgnInt.Dispose();
rgn.Dispose();
gpL.Dispose();
gpR.Dispose();
gp.Dispose();
gpLeftSmall.Dispose();
matrix.Dispose();
}
Reference:
Determine where two circles intersect

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