| public static Project ( Vector3D, vector, Vector3D, onNormal ) : Vector3D, | ||
| vector | Vector3D, | |
| onNormal | Vector3D, | |
| return | Vector3D, | |
public void Project2Test()
{
var v = new Vector3D(1.5925, 1.5075, 3);
var v2 = v.Project(new Line3D(-1.5317, 1.9230, 1.5482, 3.1248, -0.9249, -1.9787));
// v2 is endpoint of perp line from v to projection line
Assert.True(v2.EqualsTol(1e-4, -.3617, 1.2075, .6621));
}
public void Project3Test()
{
var v = new Vector3D(1, 2, 3);
var v2 = new Vector3D(4.5106, 1.8377, 0);
var vp = v.Project(v2);
Assert.True(v2.Colinear(1e-4, vp));
Assert.True(vp.EqualsTol(1e-4, 1.5565, .6341, 0));
}
/// <summary>
/// Build a perpendicular vector to this one starting from the given point p.
/// </summary>
public Line3D Perpendicular(double tol, Vector3D p)
{
if (LineContainsPoint(tol, p))
{
return(null);
}
return(new Line3D(p, p.Project(V)));
}
public void Vector3DTest_0021()
{
var tol = 1e-8;
var v1 = new Vector3D("X = 7.17678145 Y = 9.61488416 Z = 3.26614373");
var v2 = new Vector3D("X = 1.03262618 Y = 4.33930275 Z = 4.34962008");
var p = v2.Project(v1);
Assert.True(p.EqualsTol(tol, new Vector3D("X = 2.93993485 Y = 3.93869218 Z = 1.33796046")));
}
public void Project4Test()
{
// Cusago, Italy : 45,448365 E, 9,034168 N ( geodetic system )
var v = new Vector3D(9.034168, 45.448365);
// epsg3003 : monte mario / italy zone 1 ( projected system )
var epsg3003 = CRSCatalog.CRSList["EPSG:3003"];
var q = v.Project(CRSCatalog.WGS84, epsg3003);
q.EqualsTol(1e-2, 1502699.63, 5032780.63);
}
public void Project1Test()
{
var cs = new CoordinateSystem3D(
new Vector3D(6.1776, -6.3366, -5.7131), // o
new Vector3D(-2.8849, -7.6108, -1.8691), // v1
new Vector3D(-11.7294, 5.4484, 6.7873)); // v2
var v = new Vector3D(1, 2, 3);
var vp = v.Project(cs);
Assert.True(vp.EqualsTol(1e-4, -.0151, 3.0158, .4304));
}
/// <summary>
/// build 3d circle through point p, tangent to given t line, with given radius r
/// they can be two
/// </summary>
public static IEnumerable <Circle3D> CircleRTanP(double tol_len, Vector3D p, Line3D t, double r)
{
var pp = p.Project(t);
var alpha = Asin((r - pp.Distance(p)) / r);
var beta = PI / 2 - alpha;
var axisz = (p - pp).CrossProduct(t.V);
var t2 = new Line3D(p, t.V.RotateAboutAxis(axisz, beta), Line3DConstructMode.PointAndVector);
return(CirclesTan12P(tol_len, t, t2, p).Where(w => w.Radius.EqualsTol(tol_len, r)));
}
/// <summary>
/// build 3d circle that tangent to lines t1,t2 and that intersects point p
/// note: point p must contained in one of t1,t2
/// circle will be inside region t1.V toward t2.V
/// they are 4 circles
/// </summary>
public static IEnumerable <Circle3D> CirclesTan12P(double tol_len, Line3D t1, Line3D t2, Vector3D p)
{
foreach (var da in new double[] { 0, PI / 2 })
{
var ip = t1.Intersect(tol_len, t2);
var angle = t1.V.AngleRad(tol_len, t2.V);
var t3 = new Line3D(ip, t1.V.RotateAs(tol_len, t1.V, t2.V, .5, da), Line3DConstructMode.PointAndVector);
Line3D lp = null;
Line3D lNp = null;
if (t1.LineContainsPoint(tol_len, p))
{
lp = t1; lNp = t2;
}
else if (t2.LineContainsPoint(tol_len, p))
{
lp = t2; lNp = t1;
}
else
{
throw new Exception($"circle 2 tan 1 point : pt must contained in one of given tan");
}
var lpp = new Line3D(p, lp.V.RotateAboutAxis(t1.V.CrossProduct(t2.V), PI / 2), Line3DConstructMode.PointAndVector);
var c = lpp.Intersect(tol_len, t3);
var Radius = p.Distance(c);
var CS = new CoordinateSystem3D(c, lpp.V, t2.V);
yield return(new Circle3D(tol_len, CS, Radius));
// mirrored addictional circle
var mc = c.Mirror(new Line3D(p, p.Project(lNp) - p, Line3DConstructMode.PointAndVector));
yield return(new Circle3D(tol_len, new CoordinateSystem3D(mc, lpp.V, t2.V), Radius));
}
}
public Triangle2D Project(int d, ColorimetryInfo colorimetry)
{
return(new Triangle2D(_v1.Project(d), _v2.Project(d), _v3.Project(d), ApplyColorimetry(_color, colorimetry)));
}
public static Vector3D ProjectOnPlane(Vector3D vector, Vector3D planeNormal)
{
return(vector - Vector3D.Project(vector, planeNormal));
}
/// <summary>
/// Infinite line contains point.
/// </summary>
public bool LineContainsPoint(double tol, Vector3D p, bool segmentMode = false, bool excludeExtreme = false)
{
if (this.Length.EqualsTol(tol, 0))
{
return(false);
}
var prj = p.Project(this);
var dprj = p.Distance(prj);
// check if line contains point
if (dprj > tol)
{
return(false);
}
if (segmentMode)
{
// line contains given point if there is a scalar s
// for which p = From + s * V
var s = 0.0;
// to find out the scalar we need to test the first non null component
if (!(V.X.EqualsTol(tol, 0)))
{
s = (p.X - From.X) / V.X;
}
else if (!(V.Y.EqualsTol(tol, 0)))
{
s = (p.Y - From.Y) / V.Y;
}
else if (!(V.Z.EqualsTol(tol, 0)))
{
s = (p.Z - From.Z) / V.Z;
}
if (excludeExtreme)
{
if (p.EqualsTol(tol, From))
{
return(false);
}
if (p.EqualsTol(tol, To))
{
return(false);
}
return(s > 0 && s < 1);
}
else
{
// s is the scalar of V vector that runs From->To
if (s >= 0.0 && s <= 1.0)
{
return(true);
}
// point on the line but outside exact segment
// check with tolerance
if (s < 0)
{
return(p.EqualsTol(tol, From));
}
else
{
return(p.EqualsTol(tol, To));
}
}
}
return(true);
}
public static Vector3D Exclude(Vector3D excludeThis, Vector3D fromThat)
{
return(fromThat - Vector3D.Project(fromThat, excludeThis));
}
