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#Region "Microsoft.VisualBasic::c4709780fadcd0b85feef965947a8696, Microsoft.VisualBasic.Core\Language\Language\Java\Line2D.vb"
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#End Region
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Imports Point2D = System.Drawing.PointF
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Namespace Language.Java
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This class is only the abstract superclass for all objects that
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store a 2D line segment.
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The actual storage representation of the coordinates is left to
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the subclass.
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@author Jim Graham
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@since 1.2
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</summary>
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Public Module Line2D
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Returns an indicator of where the specified point
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{@code (px,py)} lies with respect to the line segment from
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{@code (x1,y1)} to {@code (x2,y2)}.
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The return value can be either 1, -1, or 0 and indicates
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in which direction the specified line must pivot around its
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first end point, {@code (x1,y1)}, in order to point at the
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specified point {@code (px,py)}.
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A return value of 1 indicates that the line segment must
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turn in the direction that takes the positive X axis towards
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the negative Y axis. In the default coordinate system used by
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Java 2D, this direction is counterclockwise.
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A return value of -1 indicates that the line segment must
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turn in the direction that takes the positive X axis towards
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the positive Y axis. In the default coordinate system, this
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direction is clockwise.
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A return value of 0 indicates that the point lies
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exactly on the line segment. Note that an indicator value
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of 0 is rare and not useful for determining collinearity
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because of floating point rounding issues.
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If the point is colinear with the line segment, but
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not between the end points, then the value will be -1 if the point
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lies "beyond {@code (x1,y1)}" or 1 if the point lies
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"beyond {@code (x2,y2)}".
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</summary>
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<param name="x1"> the X coordinate of the start point of the
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specified line segment </param>
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<param name="y1"> the Y coordinate of the start point of the
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specified line segment </param>
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<param name="x2"> the X coordinate of the end point of the
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specified line segment </param>
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<param name="y2"> the Y coordinate of the end point of the
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specified line segment </param>
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<param name="px"> the X coordinate of the specified point to be
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compared with the specified line segment </param>
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<param name="py"> the Y coordinate of the specified point to be
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compared with the specified line segment </param>
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<returns> an integer that indicates the position of the third specified
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coordinates with respect to the line segment formed
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by the first two specified coordinates.
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@since 1.2 </returns>
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Public Function relativeCCW(x1 As Double, y1 As Double, x2 As Double, y2 As Double, px As Double, py As Double) As Integer
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x2 -= x1
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y2 -= y1
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px -= x1
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py -= y1
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Dim ccw As Double = px * y2 - py * x2
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If ccw = 0.0 Then
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The point is colinear, classify based on which side of
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the segment the point falls on. We can calculate a
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relative value using the projection of px,py onto the
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segment - a negative value indicates the point projects
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outside of the segment in the direction of the particular
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endpoint used as the origin for the projection.
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ccw = px * x2 + py * y2
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If ccw > 0.0 Then
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Reverse the projection to be relative to the original x2,y2
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x2 and y2 are simply negated.
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px and py need to have (x2 - x1) or (y2 - y1) subtracted
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from them (based on the original values)
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Since we really want to get a positive answer when the
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point is "beyond (x2,y2)", then we want to calculate
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the inverse anyway - thus we leave x2 & y2 negated.
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px -= x2
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py -= y2
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ccw = px * x2 + py * y2
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If ccw < 0.0 Then ccw = 0.0
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End If
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End If
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Return If(ccw < 0.0, -1, (If(ccw > 0.0, 1, 0)))
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End Function
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Tests if the line segment from {@code (x1,y1)} to
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{@code (x2,y2)} intersects the line segment from {@code (x3,y3)}
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to {@code (x4,y4)}.
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</summary>
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<param name="x1"> the X coordinate of the start point of the first
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specified line segment </param>
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<param name="y1"> the Y coordinate of the start point of the first
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specified line segment </param>
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<param name="x2"> the X coordinate of the end point of the first
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specified line segment </param>
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<param name="y2"> the Y coordinate of the end point of the first
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specified line segment </param>
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<param name="x3"> the X coordinate of the start point of the second
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specified line segment </param>
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<param name="y3"> the Y coordinate of the start point of the second
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specified line segment </param>
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<param name="x4"> the X coordinate of the end point of the second
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specified line segment </param>
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<param name="y4"> the Y coordinate of the end point of the second
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specified line segment </param>
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<returns> <code>true</code> if the first specified line segment
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and the second specified line segment intersect
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each other; <code>false</code> otherwise.
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@since 1.2 </returns>
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Public Function linesIntersect(x1 As Double, y1 As Double, x2 As Double, y2 As Double, x3 As Double, y3 As Double, x4 As Double, y4 As Double) As Boolean
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Return ((relativeCCW(x1, y1, x2, y2, x3, y3) * relativeCCW(x1, y1, x2, y2, x4, y4) <= 0) AndAlso (relativeCCW(x3, y3, x4, y4, x1, y1) * relativeCCW(x3, y3, x4, y4, x2, y2) <= 0))
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End Function
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Returns the square of the distance from a point to a line segment.
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The distance measured is the distance between the specified
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point and the closest point between the specified end points.
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If the specified point intersects the line segment in between the
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end points, this method returns 0.0.
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</summary>
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<param name="x1"> the X coordinate of the start point of the
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specified line segment </param>
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<param name="y1"> the Y coordinate of the start point of the
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specified line segment </param>
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<param name="x2"> the X coordinate of the end point of the
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specified line segment </param>
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<param name="y2"> the Y coordinate of the end point of the
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specified line segment </param>
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<param name="px"> the X coordinate of the specified point being
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measured against the specified line segment </param>
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<param name="py"> the Y coordinate of the specified point being
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measured against the specified line segment </param>
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<returns> a double value that is the square of the distance from the
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specified point to the specified line segment. </returns>
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Public Function ptSegDistSq(x1 As Double, y1 As Double, x2 As Double, y2 As Double, px As Double, py As Double) As Double
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Adjust vectors relative to x1,y1
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x2,y2 becomes relative vector from x1,y1 to end of segment
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x2 -= x1
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y2 -= y1
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px,py becomes relative vector from x1,y1 to test point
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px -= x1
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py -= y1
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Dim dotprod As Double = px * x2 + py * y2
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Dim projlenSq As Double
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If dotprod <= 0.0 Then
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px,py is on the side of x1,y1 away from x2,y2
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distance to segment is length of px,py vector
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"length of its (clipped) projection" is now 0.0
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projlenSq = 0.0
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Else
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switch to backwards vectors relative to x2,y2
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x2,y2 are already the negative of x1,y1=>x2,y2
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to get px,py to be the negative of px,py=>x2,y2
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the dot product of two negated vectors is the same
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as the dot product of the two normal vectors
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px = x2 - px
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py = y2 - py
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dotprod = px * x2 + py * y2
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If dotprod <= 0.0 Then
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px,py is on the side of x2,y2 away from x1,y1
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distance to segment is length of (backwards) px,py vector
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"length of its (clipped) projection" is now 0.0
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projlenSq = 0.0
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Else
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px,py is between x1,y1 and x2,y2
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dotprod is the length of the px,py vector
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projected on the x2,y2=>x1,y1 vector times the
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length of the x2,y2=>x1,y1 vector
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projlenSq = dotprod * dotprod / (x2 * x2 + y2 * y2)
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End If
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End If
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Distance to line is now the length of the relative point
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vector minus the length of its projection onto the line
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(which is zero if the projection falls outside the range
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of the line segment).
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Dim lenSq As Double = px * px + py * py - projlenSq
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If lenSq < 0 Then lenSq = 0
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Return lenSq
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End Function
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Returns the distance from a point to a line segment.
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The distance measured is the distance between the specified
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point and the closest point between the specified end points.
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If the specified point intersects the line segment in between the
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end points, this method returns 0.0.
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</summary>
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<param name="x1"> the X coordinate of the start point of the
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specified line segment </param>
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<param name="y1"> the Y coordinate of the start point of the
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specified line segment </param>
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<param name="x2"> the X coordinate of the end point of the
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specified line segment </param>
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<param name="y2"> the Y coordinate of the end point of the
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specified line segment </param>
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<param name="px"> the X coordinate of the specified point being
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measured against the specified line segment </param>
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<param name="py"> the Y coordinate of the specified point being
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measured against the specified line segment </param>
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<returns> a double value that is the distance from the specified point
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to the specified line segment. </returns>
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Public Function ptSegDist(x1 As Double, y1 As Double, x2 As Double, y2 As Double, px As Double, py As Double) As Double
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Return System.Math.Sqrt(ptSegDistSq(x1, y1, x2, y2, px, py))
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End Function
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Returns the square of the distance from a point to a line.
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The distance measured is the distance between the specified
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point and the closest point on the infinitely-extended line
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defined by the specified coordinates. If the specified point
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intersects the line, this method returns 0.0.
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</summary>
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<param name="x1"> the X coordinate of the start point of the specified line </param>
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<param name="y1"> the Y coordinate of the start point of the specified line </param>
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<param name="x2"> the X coordinate of the end point of the specified line </param>
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<param name="y2"> the Y coordinate of the end point of the specified line </param>
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<param name="px"> the X coordinate of the specified point being
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measured against the specified line </param>
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<param name="py"> the Y coordinate of the specified point being
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measured against the specified line </param>
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<returns> a double value that is the square of the distance from the
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specified point to the specified line. </returns>
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Public Function ptLineDistSq(x1 As Double, y1 As Double, x2 As Double, y2 As Double, px As Double, py As Double) As Double
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Adjust vectors relative to x1,y1
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x2,y2 becomes relative vector from x1,y1 to end of segment
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x2 -= x1
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y2 -= y1
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px,py becomes relative vector from x1,y1 to test point
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px -= x1
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py -= y1
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Dim dotprod As Double = px * x2 + py * y2
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dotprod is the length of the px,py vector
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projected on the x1,y1=>x2,y2 vector times the
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length of the x1,y1=>x2,y2 vector
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Dim projlenSq As Double = dotprod * dotprod / (x2 * x2 + y2 * y2)
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Distance to line is now the length of the relative point
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vector minus the length of its projection onto the line
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Dim lenSq As Double = px * px + py * py - projlenSq
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If lenSq < 0 Then lenSq = 0
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Return lenSq
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End Function
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Returns the distance from a point to a line.
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The distance measured is the distance between the specified
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point and the closest point on the infinitely-extended line
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defined by the specified coordinates. If the specified point
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intersects the line, this method returns 0.0.
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</summary>
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<param name="x1"> the X coordinate of the start point of the specified line </param>
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<param name="y1"> the Y coordinate of the start point of the specified line </param>
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<param name="x2"> the X coordinate of the end point of the specified line </param>
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<param name="y2"> the Y coordinate of the end point of the specified line </param>
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<param name="px"> the X coordinate of the specified point being
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measured against the specified line </param>
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<param name="py"> the Y coordinate of the specified point being
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measured against the specified line </param>
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<returns> a double value that is the distance from the specified
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point to the specified line. </returns>
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Public Function ptLineDist(x1 As Double, y1 As Double, x2 As Double, y2 As Double, px As Double, py As Double) As Double
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Return System.Math.Sqrt(ptLineDistSq(x1, y1, x2, y2, px, py))
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End Function
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End Module
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End Namespace
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