TweetFollow Us on Twitter

Jul 97 Challenge

Volume Number: 13 (1997)
Issue Number: 7
Column Tag: Programmer's Challenge

Jul 97 - Programmer's Challenge

by Bob Boonstra, Westford, MA

Disambiguator

The Challenge this month is to write a string completion routine loosely patterned after the keyword lookup facility in the QuickView utility. QuickView will suggest a completion of the keyword as you begin to type it, and update that suggested completion as you continue to type. In the Toolbox Assistant, for example, if you are looking for documentation on InitGraf and type "i", the suggested completion is "iconIDToRgn". As you continue by typing "n", the suggestion becomes "index2Color". Adding "i" yields "initAllPacks"; adding "t" leaves the suggestion intact; adding "g" changes it to "initGDevice". Finally, typing "r" gives the desired "initgraf".

For our disambiguator, you will be given an unsorted list of words and an opportunity to preprocess them. Then you will be given a string to match and asked to return a list of words matching findString. To make the problem more interesting, the match string can contain wild card characters, as described below.

The prototype for the code you should write is:

typedef unsigned long ulong;

void InitDisambiguator(
   const char *const wordList[],   /* words to match against */
   ulong numWords,                 /* number of words in wordList */
   void *privStorage,              /* private storage preinitialized to zero */
   ulong storageSize               /* number of bytes of privStorage */
);

ulong /*numMatch*/ Disambiguator(
   const char *const wordList[],   /* words to match against */
   ulong numWords,                 /* number of words in wordList */
   void *privStorage,              /* private storage */
   ulong storageSize,              /* number of bytes of privStorage */
   char *findString,               /* string to match, includes wild cards */
   char *matchList[]               /* return matched words here */
);

Your InitDisambiguator routine will be called with an unsorted list wordList of numWords null-terminated words to match. The wordList words will include alphanumeric characters, spaces, and underscores. You will also be provided with a pointer privStorage to storageSize bytes of preallocated memory initialized to zero. The amount of storage provided will be at least 20 bytes for each word in wordList, plus one byte for each character in the wordList (including the null byte, and rounded up to a multiple of 4). In other words, storageSize will be no smaller than minStorage, calculated as:

for (minStorage=0,i=0; i<numWords; i++)
   minStorage += 20 + 4*(1+strlen(wordList[i])/4);

InitDisambiguator is not allowed to modify the wordList, but you may store a sorted version of wordList, or pointers to the words in sorted order, in privStorage. The first four parameters provided to Disambiguator will be identical as those provided to InitDisambiguator. In addition, you will be provided with the null-terminated findString and a preallocated array matchList with numWords entries where you are to store pointers to the words that match findString. Your string matches should be case insensitive (i.e., "initgr" matches "InitGraf". The matchList should be returned with the strings ordered in case-insensitive ASCII order (i.e., space < [0..9] < [A-Za-z] < underscore).

The findString may also contain zero or more of the wildcard characters '?', '*', and '+'. The wildcard '?' matches any single character, '*' matches zero or more characters, and '+' matches one or more characters. So, for example, "*graf" matches any string ending in the (case-insensitive) string "graf", while "+1Ind+" matches any string containing "1Ind" between the first and last characters of a word.

For each call to InitDisambiguator, your Disambiguator routine will be called an average of 100 to 1000 times. The winner will be the solution that finds the correct matchList in the minimum amount of time, including the time taken by the initialization routine.

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, or Pascal. The problem is based on a suggestion by Charles Kefauver, who pointed me to an April, 1995, AppleDirections article discussing the user interface for a disambiguator. Charles wins 2 Challenge points for his suggestion.

Three Months Ago Winner

Congratulations to ACC Murphy (Perth, Australia), for submitting the faster (and smaller) of the two entries I received for the Projection Challenge. This problem required contestants to calculate the image of a set of input polygons, including the shadows cast by one polygon on another, given an observation viewpoint and an illumination point.

Both of the submitted solutions used a ray-tracing technique. The winning solution calculates, for each point on the projection plane, the nearest polygon to the viewpoint among those intersecting the ray from the plane to the viewpoint. It then does another ray-trace to determine if there are any other polygons between the illumination point and the projected polygon, identifying the point as being in shadow if an intervening polygon is found.

I ran three test cases, moving the polygons 10 times for a given viewpoint in each case, using a GWorld bounds rectangle slightly smaller than my 1024x768 monitor. As you can see from the execution times, considerable refinement would be needed before this code could be used for animation.

A good discussion of the projection and hidden surface removal algorithms applicable to this problem can be found in the Black Art of Macintosh Game Programming, by Kevin Tieskoetter. In addition to discussing the z-buffer ray-tracing algorithm, it describes another technique for hidden surface removal called the Painter's algorithm. This approach breaks the polygons to be displayed into pieces such that each piece is entirely in front of or entirely behind any other piece, as seen from the viewpoint. The polygons can then be sorted and displayed without looking at each pixel in the image. For our application, two polygon decompositions would be required, one for the image, and one for the shadows.

The table below lists, for each entry, the execution time for each case and the code size. The number in parentheses after the entrant's name is the total number of Challenge points earned in all Challenges to date prior to this one.

                      Case 1   Case 2   Case 3    Total       Code
Name                   Time     Time     Time   Time (secs)   Size
A.C.C. Murphy (10)    29.02    23.64    81.61     134.27      4196
Ernst Munter (232)    20.87    58.11    89.76     168.74      7192

Top 20 Contestants

Here are the Top Contestants for the Programmer's Challenge. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.

Rank    Name             Points   Rank     Name             Points
   1.   Munter, Ernst      194       11.   Beith, Gary         24
   2.   Gregg, Xan         114       12.   Cutts, Kevin        21
   3.   Cooper, Greg        54       13.   Nicolle, Ludovic    21
   4.   Larsson, Gustav     47       14.   Picao, Miguel Cruz  21
   5.   Lengyel, Eric       40       15.   Brown, Jorg         20
   6.   Boring, Randy       37       16.   Gundrum, Eric       20
   7.   Mallett, Jeff       37       17.   Higgins, Charles    20
   8.   Lewis, Peter        32       18.   Kasparian, Raffi    20
   9.   Murphy, ACC         30       19.   Slezak, Ken         20
   10.  Antoniewicz, Andy   24       20.   Studer, Thomas      20

There are three ways to earn points: (1) scoring in the top 5 of any Challenge, (2) being the first person to find a bug in a published winning solution or, (3) being the first person to suggest a Challenge that I use. The points you can win are:

1st place   20 points             5th place   2 points
2nd place   10 points           finding bug   2 points
3rd place   7 points   suggesting Challenge   2 points
4th place   4 points

Here is A.C.C. Murphy's winning solution:
Challenge.p
A.C.C. Murphy

unit Challenge;

(*

Assumptions:
   Storage space must be big enough for 13 floats per polygon
   All points must be significantly smaller in magnitude than BIG_FLOAT = 
      1000000.0
   Polygons are translucent (their colour based uplon lighting is independent 
      of the side of the polygon that is lit)
   50% attenuation of colour is used
   50% attenuation of black is black
      
Method:
   InitProjection is not used
   
   First we precalculate a small bounding sphere for the polygon points.
   Next we get the information about the GWorld to allow direct pixel access.
   Then for each point on the GWorld, we trace the ray from the point to the 
      eye, intersecting it with each polygon and finding the one closes to 
      the eye (furthest forward, since the eye is infront of all polygons).  
      That determines the colour.  We then trace the ray from that intersection 
      point to the light source to determine whether the point is in shadow, 
      and if so we halve the intensity. We set the colour of the pixel and 
      move on.
   
   Optimizations:
      Direct pixel access to the GWorld (known to be 32 bit)
      Bounding sphere used to optimize the ray/polygon intersection test.
      Time is approximately 2 microseconds per pixel per polygon on an 8500.
*)

interface

   uses
      Types, Quickdraw, QDOffscreen;
      
   const
      kMAXPOINTS = 10;

   const
      BIG_FLOAT = 1000000.0;
         
   type
      float = real;
      
   type
      My2DPoint = record (* point in z==0 plane*)
         x2D: float; (* x coordinate*)
         y2D: float; (* y coordinate*)
      end;
      My3DPoint = record
         x3D: float;                 (* x coordinate*)
         y3D: float;                 (* y coordinate*)
         z3D: float;                 (* z coordinate*)
      end;
      My3DDirection = record
         thetaX:float;              (* angle in radians*)
         thetaY:float;              (* angle in radians*)
         thetaZ:float;              (* angle in radians*)
      end;
      MyPlane = record
         planeNormal: My3DDirection; (* normal vector to plane*)
         planeOrigin: My3DPoint;     (* origin of plane in 3D space*)
      end;
      MyPolygon = record
         numPoints: longint;      (* number of points in polygon*)
         thePoint: array[0..kMAXPOINTS-1] of My2DPoint;
                                  (* polygon in z==0 plane*)
         polyPlane: MyPlane;      (* rotate/translate z==0 plane to this plane*)
         polyColor: RGBColor;     (* the color to draw this polygon*)
      end;
      MyPolygonArray = array[0..0] of MyPolygon;
      
         
   procedure InitProjection(
      const viewPoint: My3DPoint;(* viewpoint from which to project*)
      const illumPoint:My3DPoint;(* viewpoint from which to draw shadow*)
      storage: univ Ptr;         (* auxiliary storage preallocated for your use*)
      storageSize: longint       (* number of bytes of storage*)
   );

   procedure CalcProjection(
      offScreen: GWorldPtr;          (* GWorld to draw projection *)
      const thePolys: MyPolygonArray;(* polygons to project *)
      numPolys: longint;             (* number of polygons to project *)
      const viewPoint: My3DPoint;    (* viewpoint from which to project *)
      const illumPoint: My3DPoint;
                               (* illumination point from which to draw shadow *)
      storage: univ Ptr;       (* auxiliary storage preallocated for your use*)
      storageSize: longint     (* number of bytes of storage*)
   );

implementation

   type
      Ray3D = record
         origin: My3DPoint;
         direction: My3DPoint;
      end;
      PolygonExtra = record
         normal, rotX, rotY, center: My3DPoint;
         radius2: float;
      end;
      PolygonExtraArray = array[0..0] of PolygonExtra;
      StorageRecord = record
         poly_extra: PolygonExtraArray;
                  { must be at the end, since it's an extensible array }
      end;
      StorageRecordPtr = ^StorageRecord;
      
   function DotProduct(const src1, src2 : My3DPoint) : float;
   begin
      DotProduct := src1.x3D*src2.x3D +  
                    src1.y3D*src2.y3D +  
                    src1.z3D*src2.z3D;
   end;
   
CrossProduct
   procedure CrossProduct(src1, src2 : My3DPoint; 
                    var dst : My3DPoint);
   begin
      dst.x3D := src1.y3D*src2.z3D - src1.z3D*src2.y3D;
      dst.y3D := src1.z3D*src2.x3D - src1.x3D*src2.z3D;
      dst.z3D := src1.x3D*src2.y3D - src1.y3D*src2.x3D;
   end;
   
AddVectors
   procedure AddVectors(const src1, src2 : My3DPoint; 
                     var dst : My3DPoint);
   begin
      dst.x3D := src1.x3D + src2.x3D;
      dst.y3D := src1.y3D + src2.y3D;
      dst.z3D := src1.z3D + src2.z3D;
   end;
      
SubtractVectors
   procedure SubtractVectors(const src1, src2 : My3DPoint; 
                      var dst : My3DPoint);
   begin
      dst.x3D := src1.x3D - src2.x3D;
      dst.y3D := src1.y3D - src2.y3D;
      dst.z3D := src1.z3D - src2.z3D;
   end;
   
MidPoint
   procedure MidPoint( const src1, src2 : My3DPoint; 
                      var dst : My3DPoint);
   begin
      dst.x3D := (src1.x3D + src2.x3D) / 2;
      dst.y3D := (src1.y3D + src2.y3D) / 2;
      dst.z3D := (src1.z3D + src2.z3D) / 2;
   end;
   
Distance2
   function Distance2( const src1, src2 : My3DPoint) : float;
   begin
      Distance2 := sqr(src1.x3D - src2.x3D) + 
                      sqr(src1.y3D - src2.y3D) + 
                      sqr(src1.z3D - src2.z3D);
   end;
   
ScaleVector
   procedure ScaleVector(const src : My3DPoint; scale : float; 
                      var dst : My3DPoint);
   begin
      dst.x3D := src.x3D * scale;
      dst.y3D := src.y3D * scale;
      dst.z3D := src.z3D * scale;
   end;
      
NormalizeVector
   procedure NormalizeVector(const src : My3DPoint;
                      var dst : My3DPoint);
      var
         length : float;
   begin
      length := sqrt(DotProduct(src,src));   
      dst.x3D := src.x3D / length;
      dst.y3D := src.y3D / length;
      dst.z3D := src.z3D / length;
   end;
   
MakeViewRay
   procedure MakeViewRay(const eye : My3DPoint;
                      x, y, z: float; var ray : Ray3D);
   begin
      ray.origin.x3D := x;
      ray.origin.y3D := y;
      ray.origin.z3D := z;
      ray.direction.x3D := eye.x3D - x;
      ray.direction.y3D := eye.y3D - y;
      ray.direction.z3D := eye.z3D - z;
      NormalizeVector(ray.direction, ray.direction);
   end;
   
RotateX
   procedure RotateX(src : My3DPoint; sinA, cosA : float; 
                      var dst : My3DPoint);
   begin
      dst.x3D := src.x3D;
      dst.y3D := cosA*src.y3D - sinA*src.z3D;
      dst.z3D := sinA*src.y3D + cosA*src.z3D;
   end;
   
RotateY
   procedure RotateY( src : My3DPoint; sinA, cosA : float; 
                      var dst : My3DPoint);
   begin
      dst.x3D := cosA*src.x3D + sinA*src.z3D;
      dst.y3D := src.y3D;
      dst.z3D := -sinA*src.x3D + cosA*src.z3D;
   end;
   
RotateZ
   procedure RotateZ( src : My3DPoint; sinA, cosA : float; 
                      var dst : My3DPoint);
   begin
      dst.x3D := cosA*src.x3D - sinA*src.y3D;
      dst.y3D := sinA*src.x3D + cosA*src.y3D;
      dst.z3D := src.z3D;
   end;
   
PointInPlaneInPolygon
   function PointInPlaneInPolygon( const pt: My2DPoint; const 
               poly: MyPolygon ): boolean;
      function Quadrant( const pt: My2DPoint; x, y: float ): 
                      longint;
      begin
         if pt.x2D > x then begin
            if pt.y2D > y then begin
               Quadrant := 0;
            end else begin
               Quadrant := 3;
            end;
         end else begin
            if pt.y2D > y then begin
               Quadrant := 1;
            end else begin
               Quadrant := 2;
            end;
         end;
      end;
      
      function x_intercept( const pt1, pt2: My2DPoint;
                      yy: float ): 
                      float;
      begin
         x_intercept := pt2.x2D - 
                     ( (pt2.y2D - yy) * 
                        ((pt1.x2D - pt2.x2D)/(pt1.y2D - pt2.y2D)) );
      end;
      
      var
         i, angle, quad, next_quad, delta: longint;
         last_vertex, next_vertex: My2DPoint;
   begin
      angle := 0;
      last_vertex := poly.thePoint[poly.numPoints-1];
      quad := Quadrant( last_vertex, pt.x2D, pt.y2D );
      for i := 1 to poly.numPoints do begin
         next_vertex := poly.thePoint[i-1];
         next_quad := Quadrant( next_vertex, pt.x2D, pt.y2D );
         delta := next_quad - quad;
         case delta of
            3: delta := -1;
            -3: delta := 1;
            2, -2: begin
               if x_intercept( last_vertex, next_vertex, pt.y2D ) > 
                           pt.x2D then begin
                  delta := -delta;
               end;
            end;
            otherwise begin
            end;
         end;
         angle := angle + delta;
         quad := next_quad;
         last_vertex := next_vertex;
      end;
      PointInPlaneInPolygon := (angle = 4) | (angle = -4);
   end;
   
Intersect
   function Intersect(const ray: Ray3D; const poly: MyPolygon; 
         const poly_extra: PolygonExtra; var distance : float; 
         var intersectionPt: My3DPoint) : boolean;
      var
         tempVector : My3DPoint;
         temp1, temp2 : float;
         intersectionPoint : My3DPoint;
         intersection2D : My2DPoint;
         Ib, Ic, Id: float;
   begin
      Intersect := false;

      { intersect ray with sphere }
      SubtractVectors( ray.origin, poly_extra.center,
                            tempVector );
      Ib := 2 * DotProduct( ray.direction, tempVector );
      Ic := DotProduct( tempVector, tempVector ) - 
                            poly_extra.radius2;
      Id := sqr(Ib) - 4.0*Ic;
      if Id >= 0 then begin { yes, ray intersects sphere }
         temp1 := DotProduct( poly.polyPlane.planeOrigin, 
                            poly_extra.normal ) - 
                     DotProduct( poly_extra.normal, ray.origin );
         temp2 := DotProduct(ray.direction, poly_extra.normal);
         if temp2 <> 0 then begin
            distance := temp1 / temp2;
            if distance > 0 then begin
               ScaleVector(ray.direction, distance, intersectionPoint);
               AddVectors(intersectionPoint, ray.origin, 
                           intersectionPoint);
               
               if Distance2(intersectionPoint, poly_extra.center)
                  <= 
                                          poly_extra.radius2 then begin 
                  { intersection point is whithin sphere.  
                     Find out if it is actually in the polygon }
                  intersectionPt := intersectionPoint;
                  { First translate back to the origin }
                  SubtractVectors(intersectionPoint, 
                     poly.polyPlane.planeOrigin,intersectionPoint);
                  intersection2D.x2D := DotProduct(
                     intersectionPoint,
                        poly_extra.rotX );
                  intersection2D.y2D := DotProduct( 
                     intersectionPoint, 
                        poly_extra.rotY );
                  { Then check if it is whithin the polygon }
                  Intersect := PointInPlaneInPolygon
                                                      (intersection2D,poly);
               end;
            end;
         end;
      end;
   end;

InitProjection
   procedure InitProjection(
      const viewPoint: My3DPoint;(* viewpoint from which to project *)
      const illumPoint:My3DPoint;
                                 (* viewpoint from which to draw shadow *)
      storage: univ Ptr;         (* auxiliary storage preallocated for your use *)
      storageSize: longint       (* number of bytes of storage *)
   );
   begin
{$unused( viewPoint, illumPoint, storage, storageSize )}
   end;

PreparsePolygons
   procedure PreparsePolygons( my_storage: StorageRecordPtr;
   numPolys: longint; const thePolys: MyPolygonArray );
      var
         i, j: longint;
         pt: My3DPoint;
         pts: array[1..kMAXPOINTS] of My3DPoint;
         min_x, min_y, min_z, max_x, max_y, max_z: My3DPoint;
         dist_x, dist_y, dist_z, new_radius2: float;
         radius, new_radius, old_to_new: float;
         sinX, cosX, sinY, cosY, sinZ, cosZ: float;
   begin
      for i := 0 to numPolys-1 do begin
         with my_storage^.poly_extra[i], thePolys[i],
         polyPlane.planeNormal do begin
            sinX := sin(thetaX);
            cosX := cos(thetaX);
            sinY := sin(thetaY);
            cosY := cos(thetaY);
            sinZ := sin(thetaZ);
            cosZ := cos(thetaZ);
            normal.x3d := sinY*cosX;
            normal.y3d := -sinX;
            normal.z3d := cosY*cosX;
            rotX.x3D := 1;
            rotX.y3D := 0;
            rotX.z3D := 0;
            RotateZ(rotX, sinZ, cosZ, rotX);
            RotateX(rotX, sinX, cosX, rotX);
            RotateY(rotX, sinY, cosY, rotX);
            rotY.x3D := 0;
            rotY.y3D := 1;
            rotY.z3D := 0;
            RotateZ(rotY, sinZ, cosZ, rotY);
            RotateX(rotY, sinX, cosX, rotY);
            RotateY(rotY, sinY, cosY, rotY);
            
            for j := 1 to numPoints do begin
               pt.x3D := thePoint[j-1].x2D;
               pt.y3D := thePoint[j-1].y2D;
               pt.z3D := 0;
               RotateZ(pt, sinZ, cosZ, pt);
               RotateX(pt, sinX, cosX, pt);
               RotateY(pt, sinY, cosY, pt);
               pts[j] := pt;
               if j = 1 then begin
                  min_x := pt; min_y := pt; min_z := pt;
                  max_x := pt; max_y := pt; max_z := pt;
               end else begin
                  if pt.x3D < min_x.x3D then begin
                     min_x := pt;
                  end;
                  if pt.y3D < min_y.y3D then begin
                     min_y := pt;
                  end;
                  if pt.z3D < min_z.z3D then begin
                     min_z := pt;
                  end;
                  if pt.x3D > max_x.x3D then begin
                     max_x := pt;
                  end;
                  if pt.y3D > max_y.y3D then begin
                     max_y := pt;
                  end;
                  if pt.z3D > max_z.z3D then begin
                     max_z := pt;
                  end;
               end;
            end;
            
            dist_x := Distance2( min_x, max_x );
            dist_y := Distance2( min_y, max_y );
            dist_z := Distance2( min_z, max_z );
            if dist_x > dist_y then begin
               if dist_x > dist_z then begin
                  radius2 := dist_x/4;
                  MidPoint( min_x, max_x, center );
               end else begin
                  radius2 := dist_z/4;
                  MidPoint( min_z, max_z, center );
               end;
            end else begin
               if dist_y > dist_z then begin
                  radius2 := dist_y/4;
                  MidPoint( min_y, max_y, center );
               end else begin
                  radius2 := dist_z/4;
                  MidPoint( min_z, max_z, center );
               end;
            end;
            
            for j := 1 to numPoints do begin
               new_radius2 := Distance2( center, pts[j] );
               if new_radius2 > radius2 then begin
                  radius := sqrt(radius2);
                  new_radius := sqrt(new_radius2);
                  radius2 := (radius + new_radius)/2;
                  old_to_new := radius2 - radius;
                  center.x3D := (radius2*center.x3D + 
                              old_to_new*pts[j].x3D)/radius;
                  center.y3D := (radius2*center.y3D + 
                              old_to_new*pts[j].y3D)/radius;
                  center.z3D := (radius2*center.z3D + 
                              old_to_new*pts[j].z3D)/radius;
                  radius2 := sqr(radius2);
               end;
            end;
         
            AddVectors( polyPlane.planeOrigin, center, center );

         end;
      end;
   end;
   
CalcProjection
   procedure CalcProjection(
      offScreen: GWorldPtr;          (* GWorld to draw projection *)
      const thePolys: MyPolygonArray;(* polygons to project *)
      numPolys: longint;             (* number of polygons to project *)
      const viewPoint: My3DPoint;    (* viewpoint from which to project *)
      const illumPoint: My3DPoint;   (* illumination point from which to draw shadow *)
      storage: univ Ptr;         (* auxiliary storage preallocated for your use *)
      storageSize: longint      (* number of bytes of storage *)
   );
      var
         bounds: Rect;
         x, y : integer;
         colour : RGBColor;
         viewRay : Ray3D;
         lightRay : Ray3D;
         i : integer;
         closestDistance : float;
         closestIntersectionPt: My3DPoint;
         thisDistance : float;
         intersectionPt: My3DPoint;
         intersect_polygon: longint;
         pm: PixMapHandle;
         junk_boolean: boolean;
         pixels: Ptr;
         rowbytes_add: longint;
         my_storage: StorageRecordPtr;
   begin
{$unused( storage, storageSize )}
      my_storage := StorageRecordPtr(storage);

      PreparsePolygons( my_storage, numPolys, thePolys );

      SetGWorld( offScreen, nil );
      bounds := offScreen^.PortRect;
      pm := GetGWorldPixMap( offScreen );
      junk_boolean := LockPixels( pm );
      pixels := GetPixBaseAddr( pm );
      rowbytes_add := band( pm^^.rowBytes, $3FFF ) - 
                                    4 * (bounds.right - bounds.left);

      for y := bounds.top to bounds.bottom-1 do begin
         for x := bounds.left to bounds.right-1 do begin
            MakeViewRay(viewPoint, x, y, 0, viewRay);
            closestDistance := 0.0;
            intersect_polygon := -1;
            for i:= 1 to numPolys do begin
               if Intersect(viewRay, thePolys[i-1], 
                           my_storage^.poly_extra[i-1], thisDistance, 
                           intersectionPt) then begin
                  if (thisDistance > closestDistance) then begin
                     intersect_polygon := i;
                     closestDistance := thisDistance;
                     closestIntersectionPt := intersectionPt;
                  end;
               end
            end;
            if intersect_polygon > 0 then begin
               colour := thePolys[intersect_polygon-1].polyColor;

               MakeViewRay(illumPoint, closestIntersectionPt.x3D, 
                                 closestIntersectionPt.y3D, 
                                 closestIntersectionPt.z3D, lightRay);

               for i:= 1 to numPolys do begin
                  if (intersect_polygon <> i) & 
                     Intersect(lightRay, thePolys[i-1], 
                     my_storage^.poly_extra[i-1], 
                     thisDistance, intersectionPt) then begin
               colour.red := band(colour.red, $0FFFF) div 2;
               colour.green := band(colour.green, $0FFFF) div 2;
               colour.blue := band(colour.blue, $0FFFF) div 2;
                     leave;
                  end
               end;
               
      LongintPtr(pixels)^ := bsl( band(colour.red, $0FF00), 8 ) 
                     + band(colour.green, $0FF00) + 
                        bsr( band(colour.blue, $0FF00), 8 );
            end else begin
               LongintPtr(pixels)^ := 0;
            end;
            longint(pixels) := longint(pixels) + 4;
         end;
         longint(pixels) := longint(pixels) + rowbytes_add;
      end;
   end;

end.

 
AAPL
$105.22
Apple Inc.
+0.39
MSFT
$46.13
Microsoft Corpora
+1.11
GOOG
$539.78
Google Inc.
-4.20

MacTech Search:
Community Search:

Software Updates via MacUpdate

OS X Server 4.0 - For OS X 10.10 Yosemit...
Designed for OS X and iOS devices, OS X Server makes it easy to share files, schedule meetings, synchronize contacts, develop software, host your own website, publish wikis, configure Mac, iPhone,... Read more
TotalFinder 1.6.12 - Adds tabs, hotkeys,...
TotalFinder is a universally acclaimed navigational companion for your Mac. Enhance your Mac's Finder with features so smart and convenient, you won't believe you ever lived without them. Tab-based... Read more
BusyCal 2.6.3 - Powerful calendar app wi...
BusyCal is an award-winning desktop calendar that combines personal productivity features for individuals with powerful calendar sharing capabilities for families and workgroups. BusyCal's unique... Read more
calibre 2.7 - Complete e-library managem...
Calibre is a complete e-book library manager. Organize your collection, convert your books to multiple formats, and sync with all of your devices. Let Calibre be your multi-tasking digital... Read more
Skitch 2.7.3 - Take screenshots, annotat...
With Skitch, taking, annotating, and sharing screenshots or images is as fun as it is simple.Communicate and collaborate with images using Skitch and its intuitive, engaging drawing and annotating... Read more
Delicious Library 3.3.2 - Import, browse...
Delicious Library allows you to import, browse, and share all your books, movies, music, and video games with Delicious Library. Run your very own library from your home or office using our... Read more
Art Text 2.4.8 - Create high quality hea...
Art Text is an OS X application for creating high quality textual graphics, headings, logos, icons, Web site elements, and buttons. Thanks to multi-layer support, creating complex graphics is no... Read more
Live Interior 3D Pro 2.9.6 - Powerful an...
Live Interior 3D Pro is a powerful yet very intuitive interior designing application. View Video Tutorials It has every feature of Live Interior 3D Standard, plus some exclusive ones: Create multi... Read more
The Hit List 1.1.7 - Advanced reminder a...
The Hit List manages the daily chaos of your modern life. It's easy to learn - it's as easy as making lists. And it's powerful enough to let you plan, then forget, then act when the time is right.... Read more
jAlbum Pro 12.2.4 - Organize your digita...
jAlbum Pro has all the features you love in jAlbum, but comes with a commercial license. With jAlbum, you can create gorgeous custom photo galleries for the Web without writing a line of code!... Read more

Latest Forum Discussions

See All

Rami Ismail Opens Up distribute​() for D...
Rami Ismail Opens Up distribute​() for Developers Posted by Jessica Fisher on October 24th, 2014 [ permalink ] Rami Ismail, Chief Executive of Business and Development at indie game studio | Read more »
Great Hitman GO Goes on Sale and Gets Ne...
Great Hitman GO Goes on Sale and Gets New Update – Say That Three Times Fast Posted by Jessica Fisher on October 24th, 2014 [ permalink ] | Read more »
Rival Stars Basketball Review
Rival Stars Basketball Review By Jennifer Allen on October 24th, 2014 Our Rating: :: RESTRICTIVE BUT FUNUniversal App - Designed for iPhone and iPad Rival Stars Basketball is a fun mixture of basketball and card collecting but its... | Read more »
Rubicon Development Makes Over a Dozen o...
Rubicon Development Makes Over a Dozen of Their Games Free For This Weekend Only Posted by Jessica Fisher on October 24th, 2014 [ permalink ] | Read more »
I Am Dolphin Review
I Am Dolphin Review By Jennifer Allen on October 24th, 2014 Our Rating: :: NEARLY FIN-TASTICUniversal App - Designed for iPhone and iPad Swim around and eat nearly everything that moves in I Am Dolphin, a fun Ecco-ish kind of game... | Read more »
nPlayer looks to be the ultimate choice...
Developed by Newin Inc, nPlayer may seem like your standard video player – but is aiming to be the best in its field by providing high quality video play performance and support for a huge number of video formats and codecs. User reviews include... | Read more »
Fighting Fantasy: Caverns of the Snow Wi...
Fighting Fantasy: Caverns of the Snow Witch Review By Jennifer Allen on October 24th, 2014 Our Rating: :: CLASSY STORYTELLINGUniversal App - Designed for iPhone and iPad Fighting Fantasy: Caverns of the Snow Witch is a sterling... | Read more »
A Few Days Left (Games)
A Few Days Left 1.01 Device: iOS Universal Category: Games Price: $3.99, Version: 1.01 (iTunes) Description: Screenshots are in compliance to App Store's 4+ age rating! Please see App Preview for real game play! **Important: Make... | Read more »
Toca Boo (Education)
Toca Boo 1.0.2 Device: iOS Universal Category: Education Price: $2.99, Version: 1.0.2 (iTunes) Description: BOO! Did I scare you!? My name is Bonnie and my family loves to spook! Do you want to scare them back? Follow me and I'll... | Read more »
Intuon (Games)
Intuon 1.1 Device: iOS Universal Category: Games Price: $.99, Version: 1.1 (iTunes) Description: Join the battle with your intuition in a new hardcore game Intuon! How well do you trust your intuition? Can you find a needle in a... | Read more »

Price Scanner via MacPrices.net

Weekend sale: 13-inch 128GB MacBook Air for $...
Best Buy has the 2014 13-inch 1.4GHz 128GB MacBook Air on sale for $849.99, or $150 off MSRP, on their online store. Choose free home shipping or free local store pickup (if available). Price valid... Read more
Nimbus Note Cross=Platform Notes Utility
Nimbus Note will make sure you never forget or lose your valuable data again. Create and edit notes, save web pages, screenshots and any other type of data – and share it all with your friends and... Read more
NewerTech’s Snuglet Makes MagSafe 2 Power Con...
NewerTech has introduced the Snuglet, a precision-manufactured ring designed to sit inside your MagSafe 2 connector port, providing a more snug fit to prevent your power cable from unintentional... Read more
Apple Planning To Sacrifice Gross Margins To...
Digitimes Research’s Jim Hsiao says its analysts believe Apple is planning to sacrifice its gross margins to save its tablet business, which has recently fallen into decline. They project that Apple’... Read more
Who’s On Now? – First Instant-Connect Search...
It’s nighttime and your car has broken down on the side of the highway. You need a tow truck right away, so you open an app on your iPhone, search for the closest tow truck and send an instant... Read more
13-inch 2.5GHz MacBook Pro on sale for $949,...
Best Buy has the 13″ 2.5GHz MacBook Pro available for $949.99 on their online store. Choose free shipping or free instant local store pickup (if available). Their price is $150 off MSRP. Price is... Read more
Save up to $125 on Retina MacBook Pros
B&H Photo has the new 2014 13″ and 15″ Retina MacBook Pros on sale for up to $125 off MSRP. Shipping is free, and B&H charges NY sales tax only. They’ll also include free copies of Parallels... Read more
Apple refurbished Time Capsules available sta...
The Apple Store has certified refurbished Time Capsules available for up to $60 off MSRP. Apple’s one-year warranty is included with each Time Capsule, and shipping is free: - 2TB Time Capsule: $255... Read more
Textilus New Word, Notes and PDF Processor fo...
Textilus is new word-crunching, notes, and PDF processor designed exclusively for the iPad. I haven’t had time to thoroughly check it out yet, but it looks great and early reviews are positive.... Read more
WD My Passport Pro Bus-Powered Thunderbolt RA...
WD’s My Passport Pro RAID solution is powered by an integrated Thunderbolt cable for true portability and speeds as high as 233 MB/s. HighlightsOverviewSpecifications Transfer, Back Up And Edit In... Read more

Jobs Board

*Apple* Solutions Consultant - Apple Inc. (U...
…important role that the ASC serves is that of providing an excellent Apple Customer Experience. Responsibilities include: * Promoting Apple products and solutions Read more
Senior Event Manager, *Apple* Retail Market...
…This senior level position is responsible for leading and imagining the Apple Retail Team's global event strategy. Delivering an overarching brand story; in-store, Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
Project Manager / Business Analyst, WW *Appl...
…a senior project manager / business analyst to work within our Worldwide Apple Fulfillment Operations and the Business Process Re-engineering team. This role will work Read more
*Apple* Retail - Multiple Positions (US) - A...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.