/*
* public static Vector2D[] Next2(Vector2D seed)
* {
* Vector2D lineUnitVector = (seed - ProjectionPoint).UnitVector;
* Vector2D linePoint = ProjectionPoint - lineUnitVector * lineUnitVector.Dot(ProjectionPoint);
* Vector2D top = linePoint + lineUnitVector * Math.Sqrt(1 - linePoint.MagnitudeSquared);
* Vector2D rotatedTop = new Vector2D(top.x / -2, top.y);
* Vector2D target = ArcLeft * rotatedTop.Dot(ArcLeft) + ArcLeft.Rotate90 * (rotatedTop.Dot(ArcLeft.Rotate90) * ScaleOut);
* Vector2D strikeThroughLineVector = (target - ScaledProjectionPoint).UnitVector;
* Vector2D strikeThroughLinePoint = ScaledProjectionPoint - strikeThroughLineVector * strikeThroughLineVector.Dot(ScaledProjectionPoint);
* Vector2D primaryScaled = strikeThroughLinePoint + strikeThroughLineVector * Math.Sqrt(1 - strikeThroughLinePoint.MagnitudeSquared);
* double distanceToScaledCenterLine = MirrorPerpendicular.Dot(primaryScaled);
* Vector2D secondaryScaled = primaryScaled - MirrorPerpendicular * (distanceToScaledCenterLine * 2);
* Vector2D primary = ArcLeft * primaryScaled.Dot(ArcLeft) + ArcLeft.Rotate90 * (primaryScaled.Dot(ArcLeft.Rotate90) * ScaleIn);
* Vector2D secondary = ArcLeft * secondaryScaled.Dot(ArcLeft) + ArcLeft.Rotate90 * (secondaryScaled.Dot(ArcLeft.Rotate90) * ScaleIn);
* return new Vector2D[] { primary, secondary };
* }
*/
/*
* public static Vector2D[] Next3(Vector2D v0)
* {
* double v0x = v0.x;
* double v0y = v0.y;
* double v1x = ProjectionPoint.x;
* double v1y = ProjectionPoint.y;
* double v2x = ArcLeft.x;
* double v2y = ArcLeft.y;
* double v3x = ScaledProjectionPoint.x;
* double v3y = ScaledProjectionPoint.y;
* double v4x = MirrorPerpendicular.x;
* double v4y = MirrorPerpendicular.y;
*
* double v5 = ScaleOut;
* double v6 = ScaleIn;
*
* double t0x = v0x - v1x;
* double t0y = v0y - v1y;
* double t0m = Math.Sqrt(t0x * t0x + t0y * t0y);
*
* double ax = t0x / t0m;
* double ay = t0y / t0m;
* double av1d = ax * v1x + ay * v1y;
*
* double bx = v1x - ax * av1d;
* double by = v1y - ay * av1d;
* double binv = Math.Sqrt(1 - bx * bx - by * by);
*
* double dx = (bx + ax * binv) / -2;
* double dy = by + ay * binv;
*
* double dv2d = dx * v2x + dy * v2y;
* double dv2drot = dx * v2y - dy * v2x;
*
* double ex = v2x * dv2d + v2y * dv2drot * v5;
* double ey = v2y * dv2d - v2x * dv2drot * v5;
*
* double t1x = ex - v3x;
* double t1y = ey - v3y;
* double t1m = Math.Sqrt(t1x * t1x + t1y * t1y);
*
* double fx = t1x / t1m;
* double fy = t1y / t1m;
* double fv3d = fx * v3x + fy * v3y;
*
* double gx = v3x - fx * fv3d;
* double gy = v3y - fy * fv3d;
* double ginv = Math.Sqrt(1 - gx * gx - gy * gy);
*
* double hx = gx + fx * ginv;
* double hy = gy + fy * ginv;
*
* double i = v4x * hx + v4y * hy;
*
* double jx = hx - v4x * i * 2;
* double jy = hy - v4y * i * 2;
*
* double hv2d = hx * v2x + hy * v2y;
* double hv2drot = hx * v2y - hy * v2x;
*
* double kx = v2x * hv2d + v2y * hv2drot * v6;
* double ky = v2y * hv2d - v2x * hv2drot * v6;
*
* double jv2d = jx * v2x + jy * v2y;
* double jv2drot = jx * v2y - jy * v2x;
*
* double lx = v2x * jv2d + v2y * jv2drot * v6;
* double ly = v2y * jv2d - v2x * jv2drot * v6;
*
* return new Vector2D[] { new Vector2D(kx,ky), new Vector2D(lx,ly) };
*
* //Mark: We are mostly interested in i. This is the distance to the centerline.
* }*/
/*
* public static Vector2D[] Next(Vector2D v0)
* {
* //Mark: i is the most interesting number. This is the distance to the centerline.
*
* //gather variables.
* double v0x = v0.x;//the seed
* double v0y = v0.y;
* double v1x = ProjectionPoint.x;
* double v1y = ProjectionPoint.y;
* double v2x = ArcLeft.x;
* double v2y = ArcLeft.y;
* double v3x = ScaledProjectionPoint.x;
* double v3y = ScaledProjectionPoint.y;
* double v4x = MirrorPerpendicular.x;
* double v4y = MirrorPerpendicular.y;
* double v5 = ScaleOut;
* double v6 = ScaleIn;
*
* //starting calculation.
* double ax = v0x - v1x;
* double ay = v0y - v1y;
* double a0 = Math.Sqrt(ax * ax + ay * ay);
*
* double bx = ax / a0;
* double by = ay / a0;
* double b0 = bx * v1x + by * v1y;
*
* //c is the base-point of the line from projectionpoint to the seed.
* double cx = v1x - bx * b0;
* double cy = v1y - by * b0;
* double c0 = Math.Sqrt(1 - cx * cx - cy * cy);
*
* //d is the rotated new target point
* double dx = (cx + bx * c0) / -2;
* double dy = cy + by * c0;
*
* double t1 = dx * v2x + dy * v2y;
* double t2 = dx * v2y - dy * v2x;
*
* //e is the scaled target
* double ex = v2x * t1 + v2y * t2 * v5;
* double ey = v2y * t1 - v2x * t2 * v5;
*
* double t3x = ex - v3x;
* double t3y = ey - v3y;
* double t3 = Math.Sqrt(t3x * t3x + t3y * t3y);
*
* double fx = t3x / t3;
* double fy = t3y / t3;
* double f0 = fx * v3x + fy * v3y;
*
* double gx = v3x - fx * f0;
* double gy = v3y - fy * f0;
* double g0 = Math.Sqrt(1 - gx * gx - gy * gy);
*
* //h is the scaled primary point
* double hx = gx + fx * g0;
* double hy = gy + fy * g0;
*
* //i is the distance to the scaled centerline.
* double i = v4x * hx + v4y * hy;
* double i2 = i * 2;
*
* //j is the scaled secondary point
* double jx = hx - v4x * i2;
* double jy = hy - v4y * i2;
*
* double h0 = hx * v2x + hy * v2y;
* double h1 = (hx * v2y - hy * v2x)*v6;
*
* //k is the unscaled primary point
* double kx = v2x * h0 + v2y * h1;
* double ky = v2y * h0 - v2x * h1;
*
* double j0 = jx * v2x + jy * v2y;
* double j1 = (jx * v2y - jy * v2x)*v6;
*
* //l the unscaled secondary point
* double lx = v2x * j0 + v2y * j1;
* double ly = v2y * j0 - v2x * j1;
*
* return new Vector2D[] { new Vector2D(kx, ky), new Vector2D(lx, ly) };
* }
*/
public static ScaledCenterlinePair NextBasic(Vector2D v0, long index)
{
//gather variables.
double v0x = v0.x;//the seed
double v0y = v0.y;
//starting calculation.
double ax = v0x - v1x;
double ay = v0y - v1y;
double a0 = Math.Sqrt(ax * ax + ay * ay);
double bx = ax / a0;
double by = ay / a0;
double b0 = bx * v1x + by * v1y;
//c is the base-point of the line from projectionpoint to the seed.
double cx = v1x - bx * b0;
double cy = v1y - by * b0;
double c0 = Math.Sqrt(1 - cx * cx - cy * cy);
//d is the rotated new target point
double dx = (cx + bx * c0) / -2;
double dy = cy + by * c0;
double t1 = dx * v2x + dy * v2y;
double t2 = dx * v2y - dy * v2x;
//e is the scaled target
double ex = v2x * t1 + v2y * t2 * v5;
double ey = v2y * t1 - v2x * t2 * v5;
double t3x = ex - v3x;
double t3y = ey - v3y;
double t3 = Math.Sqrt(t3x * t3x + t3y * t3y);
double fx = t3x / t3;
double fy = t3y / t3;
double f0 = fx * v3x + fy * v3y;
double gx = v3x - fx * f0;
double gy = v3y - fy * f0;
double g0 = Math.Sqrt(1 - gx * gx - gy * gy);
//h is the scaled primary point
double hx = gx + fx * g0;
double hy = gy + fy * g0;
//i is the distance to the scaled centerline.
double i = v4x * hx + v4y * hy;
double i2 = i * 2;
//j is the scaled secondary point
double jx = hx - v4x * i2;
double jy = hy - v4y * i2;
double h0 = hx * v2x + hy * v2y;
double h1 = (hx * v2y - hy * v2x) * v6;
//k is the unscaled primary point
double kx = v2x * h0 + v2y * h1;
double ky = v2y * h0 - v2x * h1;
double j0 = jx * v2x + jy * v2y;
double j1 = (jx * v2y - jy * v2x) * v6;
//l the unscaled secondary point
double lx = v2x * j0 + v2y * j1;
double ly = v2y * j0 - v2x * j1;
ScaledCenterlinePair result = new ScaledCenterlinePair()
{
distanceToScaledCenterLine = i,
primary = new Vector2D(kx, ky),
secondary = new Vector2D(lx, ly),
primaryIndex = index << 1,
secondaryIndex = index << 1 | 1
};
return(result);
}
/*
* private void TestMinimal2Button_Click(object sender, EventArgs e)
* {
* MinimalEquation.Initialize();
* Vector3D[] first = MinimalEquation.NextEquational(MinimalEquation.FirstSeedE);
* }*/
private void GeodesicAnalysisButton_Click(object sender, EventArgs e)
{
using (SaveFileDialog sfd = new SaveFileDialog()
{
Filter = "*.csv|*.csv"
})
{
if (sfd.ShowDialog() != DialogResult.OK)
{
return;
}
List <ScaledCenterlinePair> current = new List <ScaledCenterlinePair>();
List <ScaledCenterlinePair> next = new List <ScaledCenterlinePair>();
MinimalEquation.Initialize();
Vector2D seed = MinimalEquation.FirstSeed;
ScaledCenterlinePair basicSet = new ScaledCenterlinePair();
basicSet.primary = seed;
basicSet.distanceToScaledCenterLine = 0;
basicSet.primaryIndex = 1;
current.Add(basicSet);
List <string> lines = new List <string>();
string header = "Count;Index;IndexBin;Distance;X;Y;";
lines.Add(header);
long i = 1;
long generations = Convert.ToInt32(GenerationBox.Text);
for (int g = -1; g < generations; g++)
{
foreach (ScaledCenterlinePair set in current)
{
string line = i.ToString() + ";";
i++;
line += set.primaryIndex.ToString() + ";";
line += Convert.ToString(set.primaryIndex, 2) + ";";
line += (-set.distanceToScaledCenterLine).ToString() + ";";
line += set.primary.x.ToString() + ";";
line += set.primary.y.ToString() + ";";
lines.Add(line);
line = "";
if (set.secondary != null)
{
line += i.ToString() + ";";
i++;
line += set.secondaryIndex.ToString() + ";";
line += Convert.ToString(set.secondaryIndex, 2) + ";";
line += set.distanceToScaledCenterLine.ToString() + ";";
line += set.secondary.x.ToString() + ";";
line += set.secondary.y.ToString() + ";";
lines.Add(line);
}
if (g < generations - 1)
{
next.Add(MinimalEquation.NextBasic(set.primary, set.primaryIndex));
if (set.secondary != null)
{
next.Add(MinimalEquation.NextBasic(set.secondary, set.secondaryIndex));
}
}
}
current = next;
next = new List <ScaledCenterlinePair>();
}
File.WriteAllLines(sfd.FileName, lines);
}
}