function selectByDistance(Point selector, 
                          Point target, 
                          double distance)
 {                                        
  for (value i = 0; i < target.Count; ++i)
   {                                            
    if (Distance(selector,target[i]) < distance)
     {
      Point result= new Point(this);
      result.ByCartesianCoordinates(baseCS, 
                                    target[i].X, 
                                    target[i].Y, 
                                    target[i].Z);
     }
   }
 };		

selectByDistance(selector,target,distance);		

Distance between Points Select points from a collection depending on their distance to a selector point. First write a function\index{function} a condition for target points to be selected. In this sample example, the distance between the target and the selector point must be less than variable $d$. Write a behaviour function that checks the target points one by one and compares the distance between each point and the selector point using the threshold $d$. For each member of the list, if the condition is satisfied, the selector function creates a copy of the target point. The behaviour function returns a new list of result points that are within distance $d$ of the selector point. Note that the structure of the target and result my differ. For instance, the target may be a 2D array\index{data structure!array} and the result a 1D array. You have to make and remember such choices. Click to download SeleDistanceBetweenPoints.gct Part of Curve Select part of a curve depending on its distance to a point. Place a collection of parametric points\index{point} on the curve\index{curve}. Use the same mechanism for selecting these points as in the sample Distance between Points. Write a function that checks each of the points and reports them if they satisfy the condition. Placing a curve through the selected points yields an approximate copy of part of the original curve. Moving the selector point, controls the part of the curve to be copied. The more points on the original curve, the more accurate the selected curve. The original points sample the curve and so will not generally capture the exact point on the curve that is at the specified distance. This problem may be addressed by searching between the last selected point and the first non-selected point for the point at which the distance to the selector is exactly the threshold. If, however, the original points are widely spaced, very small sections of the curve that are within the threshold might fail to be detected. This can be addressed by projecting\index{transformation!projection} the selector point onto the curve. If the distance to the selector point is less than than the threshold, search on either side of the projected point for the exact end points of the curve. Click to download SelePartOfACurve.gct Lines inside Curve Select all lines that are completely inside a closed curve. This Selector has two parts. First, if a line\index{line!segment} segment is entirely inside or outside a curve\index{curve} it does not intersect the curve. In order to check the position of a line against a curve, first compute the intersection. If the result is null, the line may be either inside or outside. \begin{bodyNote} \pbOneCol { \input{\GCFigsPath/Patterns/SeleJordanCurve10.tex} \input{\GCFigsPath/Patterns/SeleJordanCurve20.tex} } \end{bodyNote} Second, if an endpoint of a non-intersecting line is inside the curve, so is the line. The Jordan Curve theorem\index{Jordan Curve theorem} states that a point is inside a closed curve if a line segment between the point and anther points external to the curve intersects the curve an odd number of times. Use the Jordan Curve theorem to determine the position of either end of the line segment against the closed curve. Don't count tangencies as crossings! If the number of intersections is odd, the line is inside the curve. \begin{bodyNote} \pbOneCol { \input{\GCFigsPath/Patterns/SeleJordanCurve30.tex} \input{\GCFigsPath/Patterns/SeleJordanCurve40.tex} } \end{bodyNote} Write a function\index{function} that performs both of the above tests in turn. If both succeed (non-intersection of the segment and odd intersections of a ray from an end point) copy and return the line. Click to download SeleLinesInsideCurve.gct Points inside Sector Select the points\index{point} that lie inside a 2D sector (two vectors bound to a common point). The sector comprises a base point and two vectors $u$ and $v$ bound to it. Taken in order, these define an angle between $0$ and $360\; degrees$. Imagine a target vector $a$ for each target point connecting from the base point to the target point. Take the two cross products\index{vector!cross product} $$ and $$. Remember from Section \ref{sec:Frames:cross-prod} that the right hand rule\index{frame!right hand rule} determines the orientation of the cross product of two vectors. If the angle between the vectors $u$ and $v$ is less than $180\; degrees$, a target point is between two selector vectors if the $z$-components of both the cross products of its vector with the selector vectors are positive. If the angle\index{angle} is greater than $180\; degrees$, the target point is in the sector if one or both of the cross products are positive. \begin{bodyNote} \pbOneCol { \input{\GCFigsPath/Geometry/crossProductInLt180.tex} \input{\GCFigsPath/Geometry/crossProductOutLt180.tex} } \vspace{3mm} \pbOneCol { \input{\GCFigsPath/Geometry/crossProductInReflex.tex} \input{\GCFigsPath/Geometry/crossProductOutReflex.tex} } \end{bodyNote} The scalar product\index{vector!scalar product} determines if the sector given by the base point and $u$ and $v$ is greater than $180\; degrees$. If the sector is between $0s$ and $180\; degrees$, $u.v$ is positive. If the sector is between $180$ and $360\; degrees$, $u.v$ is negative. When $u$ and $v$ are colinear, the sector is either $0\; degrees$ ($u.v\; >\; =\; 0$) or $180\; degrees$ (). The selector function\index{function} iterates over the target points\index{point} one by one. For each point, it computes the two cross products\index{vector!cross product}$$ and $$. Using the rules above it determines if each point lies within the sector and includes each successful point in the result. Click to download SelePointsInsideSector.gct Click to download SelePointsInside3DSector.gct Points inside Box Select points that are inside a box. Write a behaviour function\index{function} that checks the position of the target points\index{point} against the box. The function reports their position in the coordinate system\index{frame} of the selector box one by one and compares their new coordinates to two opposite corners of the box. The function then reports them in the result list if they are inside the box. Click to download SelePointsInsideBox.gct \renewcommand{\sampleNewPage}[0]{false} Length of Line Select lines based on their length. Given a list of lines\index{line}, select those whose lengths are equal to a variable, equal to the length of a selector line, or between the lengths of two selector lines. Use a function\index{function} that iterates through the target lines. For each target line, if it has the desired length, the function reports it and puts it in a new list of result lines. Click to download SeleLengthOfLine.gct Boundary To be added. To be added. Click to download SeleBoundary.gct