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Cleaned-up the trigonometry class.
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@sonomirco
sonomirco committed Jan 5, 2023
1 parent 5ed89e7 commit 80972de
Showing 1 changed file with 32 additions and 49 deletions.
81 changes: 32 additions & 49 deletions src/GShark/Core/Trigonometry.cs
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Original file line number Diff line number Diff line change
@@ -1,29 +1,24 @@
using GShark.Geometry;
using System;
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Linq;
using GShark.Geometry;

namespace GShark.Core
{
/// <summary>
/// Provides basic trigonometry methods.
/// Provides basic trigonometry methods.
/// </summary>
public class Trigonometry
{
/// <summary>
/// Determines if the provide points are on the same plane within specified tolerance.
/// Determines if the provide points are on the same plane within specified tolerance.
/// </summary>
/// <param name="points">Points to check.</param>
/// <param name="tolerance">Tolerance.</param>
/// <returns>True if all points are coplanar.</returns>
public static bool ArePointsCoplanar(IList<Point3> points, double tolerance = GSharkMath.Epsilon)
{
// https://en.wikipedia.org/wiki/Triple_product
if (points.Count <= 3)
{
return true;
}
if (points.Count <= 3) return true;

var vec1 = points[1] - points[0];
var vec2 = points[2] - points[0];
Expand All @@ -32,19 +27,16 @@ public static bool ArePointsCoplanar(IList<Point3> points, double tolerance = GS
{
var vec3 = points[i] - points[0];
double tripleProduct = Vector3.DotProduct(Vector3.CrossProduct(vec3, vec2), vec1);
if (Math.Abs(tripleProduct) > GSharkMath.Epsilon)
{
return false;
}
if (Math.Abs(tripleProduct) > GSharkMath.Epsilon) return false;
}

return true;
}

/// <summary>
/// Determines if three points form a straight line (are collinear) within a given tolerance.<br/>
/// Find the area of the triangle without using square root and multiply it for 0.5.<br/>
/// http://www.stumblingrobot.com/2016/05/01/use-cross-product-compute-area-triangles-given-vertices/
/// Determines if three points form a straight line (are collinear) within a given tolerance.<br />
/// Find the area of the triangle without using square root and multiply it for 0.5.<br />
/// http://www.stumblingrobot.com/2016/05/01/use-cross-product-compute-area-triangles-given-vertices/
/// </summary>
/// <param name="pt1">First point.</param>
/// <param name="pt2">Second point.</param>
Expand All @@ -62,7 +54,8 @@ public static bool ArePointsCollinear(Point3 pt1, Point3 pt2, Point3 pt3, double
}

/// <summary>
/// Calculates the point at the equal distance from the three points, it can be also described as the center of a circle.
/// Calculates the point at the equal distance from the three points, it can be also described as the center of a
/// circle.
/// </summary>
/// <param name="pt1">First point.</param>
/// <param name="pt2">Second point.</param>
Expand All @@ -88,8 +81,8 @@ public static Point3 EquidistantPoint(Point3 pt1, Point3 pt2, Point3 pt3)
}

/// <summary>
/// Gets the orientation between tree points in the plane.<br/>
/// https://math.stackexchange.com/questions/2386810/orientation-of-three-points-in-3d-space
/// Gets the orientation between tree points in the plane.<br />
/// https://math.stackexchange.com/questions/2386810/orientation-of-three-points-in-3d-space
/// </summary>
/// <param name="pt1">First point.</param>
/// <param name="pt2">Second point.</param>
Expand All @@ -101,58 +94,47 @@ public static int PointOrder(Point3 pt1, Point3 pt2, Point3 pt3)
Vector3 n = Vector3.CrossProduct(pt2 - pt1, pt3 - pt1);
double result = Vector3.DotProduct(pl.ZAxis, n.Unitize());

if (Math.Abs(result) < GSharkMath.Epsilon)
{
return 0;
}
if (Math.Abs(result) < GSharkMath.Epsilon) return 0;

return (result < 0) ? 1 : 2;
return result < 0 ? 1 : 2;
}

/// <summary>
/// Finds the closest point on a segment.<br/>
/// It is not a segment like a line or ray but the part that compose the segment.<br/>
/// The segment is deconstruct in two points and two t values.
/// Finds the closest point on a segment.<br />
/// It is not a segment like a line or ray but the part that compose the segment.<br />
/// The segment is deconstruct in two points and two t values.
/// </summary>
/// <param name="point">Point to project.</param>
/// <param name="segmentPt0">First point of the segment.</param>
/// <param name="segmentPt1">Second point of the segment.</param>
/// <param name="valueT0">First t value of the segment.</param>
/// <param name="valueT1">Second t value of the segment.</param>
/// <returns>Tuple with the closest point its corresponding tValue on the curve.</returns>
public static (double tValue, Point3 pt) ClosestPointToSegment(Point3 point, Point3 segmentPt0, Point3 segmentPt1, double valueT0, double valueT1)
public static (double tValue, Point3 pt) ClosestPointToSegment(Point3 point, Point3 segmentPt0,
Point3 segmentPt1, double valueT0, double valueT1)
{
Vector3 direction = segmentPt1 - segmentPt0;
double length = direction.Length;

if (length < GSharkMath.Epsilon)
{
return (tValue: valueT0, pt: segmentPt0);
}
if (length < GSharkMath.Epsilon) return (tValue: valueT0, pt: segmentPt0);

Vector3 vecUnitized = direction.Unitize();
Vector3 ptToSegPt0 = point - segmentPt0;
double dotResult = Vector3.DotProduct(ptToSegPt0, vecUnitized);

if (dotResult < 0.0)
{
return (tValue: valueT0, pt: segmentPt0);
}
if (dotResult < 0.0) return (tValue: valueT0, pt: segmentPt0);

if (dotResult > length)
{
return (tValue: valueT1, pt: segmentPt1);
}
if (dotResult > length) return (tValue: valueT1, pt: segmentPt1);

Point3 pointResult = segmentPt0 + (vecUnitized * dotResult);
Point3 pointResult = segmentPt0 + vecUnitized * dotResult;
double tValueResult = valueT0 + (valueT1 - valueT0) * dotResult / length;
return (tValue: tValueResult, pt: pointResult);
}

/// <summary>
/// Calculates the area of a triangle.
/// The calculation use the Heron's formula.
/// https://en.wikipedia.org/wiki/Heron%27s_formula
/// Calculates the area of a triangle.
/// The calculation use the Heron's formula.
/// https://en.wikipedia.org/wiki/Heron%27s_formula
/// </summary>
/// <param name="pt1">First point of the triangle.</param>
/// <param name="pt2">Second point of the triangle.</param>
Expand All @@ -165,18 +147,19 @@ public static double AreaOfTriangle(Point3 pt1, Point3 pt2, Point3 pt3)
double distC = pt3.DistanceTo(pt1);

double semiperimeter = (distA + distB + distC) / 2;
return Math.Sqrt(semiperimeter * (semiperimeter - distA) * (semiperimeter - distB) * (semiperimeter - distC));
return Math.Sqrt(
semiperimeter * (semiperimeter - distA) * (semiperimeter - distB) * (semiperimeter - distC));
}

/// <summary>
/// Calculates the area of a triangle defined as a polyline.
/// Calculates the area of a triangle defined as a polyline.
/// </summary>
/// <param name="polyLine">The polyline.</param>
/// <returns>The area of the triangle.</returns>
public static double AreaOfTriangle(PolyLine polyLine)
{
var pts = polyLine.ControlPointLocations;
var pts = polyLine.ControlPointLocations;
return AreaOfTriangle(pts[0], pts[1], pts[2]);
}
}
}
}

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