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calculate Triangle Circumcircle And Inscribed_Circle/InCircle

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Hi... I want to calculate Triangle Circumcircle And Inscribed_Circle/InCircle in 3D space.... if anybody know C/java code please give me link of that code...remember in 3D space... please help me.. THanks..

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This is how it works in general:

Assuming a triangle consisting of three points A, B and C

Circumcircle:
- find the points halfway on AB and AC (AB being the segment between A and B, AC being the segment between A and C)
- create perpendicular lines on AB and AC in those points
- the intersection between those two lines is the centerpoint of the circumcircle
- the radius is the distance between the center point and any of the three points A, B and C

Incircle:
- create the bisecting line in two points, e.g. A and B
- the intersection of those lines is the center point of the incircle
- the radius is given by the distance between the centerpoint and any of the three triangle sides.

Here's some code (it's in C#, but it should be readable)

Circumcircle:

// lines from a to b and a to c
var AB = B - A;
var AC = C - A;

// perpendicular vector on triangle
var N = Vector3.Normalize(Vector3.Cross(AB, AC));

// find the points halfway on AB and AC
var halfAB = A + AB*0.5f;
var halfAC = A + AC*0.5f;

// build vectors perpendicular to ab and ac
var perpAB = Vector3.Cross(AB, N);
var perpAC = Vector3.Cross(AC, N);

// find intersection between the two lines
// D: halfAB + t*perpAB
// E: halfAC + s*perpAC
var center = LineLineIntersection(halfAB, perpAB, halfAC, perpAC);
// the radius is the distance between center and any point
// distance(A, B) = length(A-B)
var radius = Vector3.Distance(center, A);






Incircle

// create bisecting lines in a and b
var AB = Vector3.Normalize(B - A);
var AC = Vector3.Normalize(C - A);
var bisectADir = AB + AC;

var BA = Vector3.Normalize(A - B);
var BC = Vector3.Normalize(C - B);
var bisectBDir =BA + BC;

// find intersection => center point of incircle
var center = LineLineIntersection(A, bisectADir, B, bisectBDir);
// find distance to any side => radius
var radius = PointLineDistance(center, A, B - A);






And the two helper methods LineLineIntersection and PointLineDistance:


/// <summary>
/// Calculates the intersection point between two lines, assuming that there is such a point.
/// </summary>
/// <param name="originD">The origin of the first line</param>
/// <param name="directionD">The direction of the first line.</param>
/// <param name="originE">The origin of the second line.</param>
/// <param name="directionE">The direction of the second line.</param>
/// <returns>The point at which the two lines intersect.</returns>
Vector3 LineLineIntersection(Vector3 originD, Vector3 directionD, Vector3 originE, Vector3 directionE) {
directionD.Normalize();
directionE.Normalize();
var N = Vector3.Cross(directionD, directionE);
var SR = originD - originE;
var absX = Math.Abs(N.X);
var absY = Math.Abs(N.Y);
var absZ = Math.Abs(N.Z);
float t;
if (absZ > absX && absZ > absY) {
t = (SR.X*directionE.Y - SR.Y*directionE.X)/N.Z;
} else if (absX > absY) {
t = (SR.Y*directionE.Z - SR.Z*directionE.Y)/N.X;
} else {
t = (SR.Z*directionE.X - SR.X*directionE.Z)/N.Y;
}
return originD - t*directionD;
}

/// <summary>
/// Calculates the distance between a point and a line.
/// </summary>
/// <param name="P">The point.</param>
/// <param name="S">The origin of the line.</param>
/// <param name="D">The direction of the line.</param>
/// <returns>
/// The distance of the point to the line.
/// </returns>
float PointLineDistance(Vector3 P, Vector3 S, Vector3 D) {
D.Normalize();
var SP = P - S;
return Vector3.Distance(SP, Vector3.Dot(SP, D)*D);
}






Vector3 is some 3D float vector implementation providing default vector operations such as addition, scaling, dot product and cross product.

Here's a screenshot of an app using the code above:

Free Image Hosting at www.ImageShack.us
thank u very much sir.....

its gr8.....


---------------------


can u tell me about this....following routine doesn't use intersection but its for 2D...





-----------------------------




// converts trilinear coordinates to Cartesian coordinates relative
// to the incenter; thus, the incenter has coordinates (0.0, 0.0)
public Coordinate toCartesian(double alpha, double beta, double gamma)
{
double area = getArea();
double as = getSideA(), bs = getSideB(), cs = getSideC();
double r = 2 * area / (as + bs + cs);
double k = 2 * area / (as*alpha + bs*beta + cs*gamma);
double cosC = Math.cos(getAngleC()), sinC = Math.sin(getAngleC());




//Look At here..
//this routine is very very simple...but here how can we find Z coordinate...here we only need a one formula for determine the Z coordinate...can we fine Z??????

//-------------------------------------------------------------------

double x = (k*beta - r + (k*alpha - r)*cosC) / sinC;
double y = k*alpha - r;

double z = ???????????????????????????????????????????

//-------------------------------------------------------------------

return new Coordinate(x, y);
}

// calculates the circumradius
public Circle getCircumcircle()
{
double cosA = Math.cos(getAngleA());
double cosB = Math.cos(getAngleB());
double cosC = Math.cos(getAngleC());
Coordinate center = toCartesian(cosA, cosB, cosC);
double as = getSideA(), bs = getSideB(), cs = getSideC();
double s = 0.5 * (as + bs + cs);
double radius = (as * bs * cs) / (4 * Math.sqrt(
s * (as + bs - s) * (as + cs - s) * (bs + cs - s)));
return new Circle(center, radius);
}

// calculates the inradius
public Circle getIncircle()
{
Coordinate center = toCartesian(1.0, 1.0, 1.0);
double as = getSideA(), bs = getSideB(), cs = getSideC();
double semiperimeter = 0.5 * (as + bs + cs);
double radius = getArea() / semiperimeter;
return new Circle(center, radius);
}



[/edit]


thanks..

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