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.

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Bean 3.3.1 - Fast and uncluttered word p...
Bean is no longer being actively developed, but will be updated as necessary to patch bugs and maintain OS X compatibility Bean is lean, fast, and uncluttered. If you get depressed at the thought... Read more
RetroArch 1.9.0 - Game emulator.
RetroArch is most popularly known for being a program with which you can play many emulators and games, which have all been customized and tailor-ported to the libretro API. It is designed to be fast... Read more
NetNewsWire 5.0.4 - RSS and Atom news re...
NetNewsWire is the best way to keep up with the sites and authors you read most regularly. Let NetNewsWire pull down the latest articles, and read them in a distraction-free and Mac-like way. Native... Read more
EarthDesk 7.4.5 - $24.99
EarthDesk replaces your static desktop picture with a rendered image of Earth showing correct sun, moon, and city illumination. With an Internet connection, EarthDesk displays near-real-time global... Read more
BetterTouchTool 3.401 - Customize multi-...
BetterTouchTool adds many new, fully customizable gestures to the Magic Mouse, Multi-Touch MacBook trackpad, and Magic Trackpad. These gestures are customizable: Magic Mouse: Pinch in / out (zoom)... Read more
Vienna 3.5.6 :e12c952d: - RSS and Atom n...
Vienna is a freeware and Open-Source RSS/Atom newsreader with article storage and management via a SQLite database, written in Objective-C and Cocoa, for the OS X operating system. It provides... Read more
WhatsApp 2.2031.5 - Desktop client for W...
WhatsApp is the desktop client for WhatsApp Messenger, a cross-platform mobile messaging app which allows you to exchange messages without having to pay for SMS. WhatsApp Messenger is available for... Read more
Day One 4.16 - Maintain a daily journal.
Day One is an easy, great-looking way to use a journal / diary / text-logging application. Day One is well designed and extremely focused to encourage you to write more through quick Menu Bar entry,... Read more
VMware Fusion 11.5.6 - Run Windows apps...
VMware Fusion and Fusion Pro - virtualization software for running Windows, Linux, and other systems on a Mac without rebooting. The latest version includes full support for Windows 10, macOS Mojave... Read more
Alfred 4.1 - Quick launcher for apps and...
Alfred is an award-winning productivity application for OS X. Alfred saves you time when you search for files online or on your Mac. Be more productive with hotkeys, keywords, and file actions at... Read more

Latest Forum Discussions

See All

Motorball is a car football game from No...
A few years back Noodlecake Studios announced that they would be dipping in the multiplayer gaming realm with two different games. The first of those, Golf Blitz, released a while back and has proven to be very popular. Now, the second has arrived... | Read more »
SINoALICE's latest update introduce...
SINoALICE's latest update has now arrived, adding several fan-favourite characters from popular RPG series NieR. Young Nier, Kaine, and Young Emil are available in-game as part of a limited-time crossover event set to run until August 20th. [Read... | Read more »
Rocat Jumpurr is an intense roguelite pl...
Rocat Jumpurr is a roguelite platformer from developer Mousetrap Games. You might already be familiar with it if you follow the Big Indie Pitch, where it won first place during this year's Pocket Gamer Connects London competition. Following its... | Read more »
PUBG Mobile's Play As One campaign...
Back in mid-July, we reported that PUGB Mobile had teamed up with Direct Relief to help raise money for the charity's COVID-19 response project. It focused on an in-game running challenge for players, which lead to the PUBG Mobile donating $2... | Read more »
Marvel Contest of Champions' latest...
Marvel Contest of Champions' latest motion comic has arrived, and it shows off new fighters Air-Walker and Dragon Man. Both characters are set to arrive in-game this month. [Read more] | Read more »
Clash Royale: The Road to Legendary Aren...
Supercell recently celebrated its 10th anniversary and their best title, Clash Royale, is as good as it's ever been. Even for lapsed players, returning to the game is as easy as can be. If you want to join us in picking the game back up, we've put... | Read more »
Global Spy is an intriguing 2D spy sim f...
Developer Yuyosoft Innovations' Global Spy launched last month for iOS and Android, though if you missed it at the time, we're here to tell you why it's well worth a go. This one's all about international espionage, tracking down elusive spies,... | Read more »
Distract Yourself With These Great Mobil...
There’s a lot going on right now, and I don’t really feel like trying to write some kind of pithy intro for it. All I’ll say is lots of people have been coming together and helping each other in small ways, and I’m choosing to focus on that as I... | Read more »
Hyena Squad is sci-fi turn-based strateg...
Wave Light Games has just revealed its latest release, Hyena Squad, a turn-based RPG set in a space station infested by gross aliens and the living dead. The announcement was first reported on by Touch Arcade. [Read more] | Read more »
Idle Guardians: Never Die is a pixel art...
SuperPlanet has been fairly prolific with game releases so far this year with both Evil Hunter Tycoon and Lucid Adventure releasing earlier this year. Now, they've released another idle RPG called Idle Guardians: Never Die, which you can download... | Read more »

Price Scanner via MacPrices.net

Sale! Apple’s 16″ MacBook Pros for up to $349...
Apple Authorized Reseller Adorama has new 2019 16″ MacBook Pros in stock on sale today for $100-$349 off Apple’s MSRP, each including free shipping. Their prices for 8-core models ($349 off) are the... Read more
Save hundreds of dollars on a custom-configur...
Save up to $920 on a custom-configured 16″ MacBook Pro with these Certified Refurbished models that Apple has restocked today. Each MacBook Pro features a new outer case, free shipping, and includes... Read more
New 2020 12.9″ iPad Pros on sale for up to $8...
Apple reseller Expercom has new 2020 Apple 12.9″ iPad Pros on sale today for $60-$85 off MSRP, with prices starting at $939. These are the same iPad Pros sold by Apple in their retail and online... Read more
Woot offers numerous 2018-2020 MacBook Pros a...
Amazon-owned Woot has many open-box return MacBook Airs and MacBook Pros available today at prices starting at $879. Shipping is free for Prime members. Here’s what they have as of this post, and... Read more
Apple restocks refurbished 2020 13″ MacBook A...
Apple has restocked Certified Refurbished 2020 13″ MacBook Airs starting at only $849 and up to $200 off the cost of new Airs. Each MacBook features a new outer case, comes with a standard Apple one-... Read more
Apple restocks clearance 2019 13″ 2.4GHz MacB...
Apple has restocked Certified Refurbished 2019 13″ 2.4GHz 4-Core Touch Bar MacBook Pros starting at $1359 and up to $560 off original MSRP. Apple’s one-year warranty is included, shipping is free,... Read more
Apple restocks refurbished iPhone XR models s...
Apple has restocked Certified Refurbished, unlocked, iPhone XR models in the refurbished section of their online store starting at $539. Each iPhone comes with Apple’s standard one-year warranty,... Read more
Price drops! $100-$200 off clearance 27″ 5K i...
B&H Photo has dropped prices on clearance, previous-generation 27″ 5K iMacs by up to $200 off Apple’s original MSRP: – 27″ 3.0GHz 6-Core 5K iMac: $1699 $100 off original MSRP – 27″ 3.1GHz 6-Core... Read more
Woot offers Apple Watch and iPhone models fro...
Amazon-owned Woot has refurbished Apple Watch and iPhone models available from $99-$749 through August 6th. According to Woot, the items may show some wear, but they have all been fully tested and... Read more
Apple’s Phil Schiller Steps Down As SVP OF Wo...
NEWS: 08.05.20 – Former Apple senior Vice President of worldwide marketing, Phil Schiller, is stepping down from his long time role at the company in order to focus on spending more time with family... Read more

Jobs Board

Cub Foods - *Apple* Valley - Now Hiring Par...
Cub Foods - Apple Valley - Now Hiring Part Time! United States of America, Minnesota, Apple Valley New Retail Post Date 5 days ago Requisition # 122305 Sign Up Read more
Blue *Apple* Cafe Student Worker - Fall - P...
…to enhance your work experience. Student positions are available at the Blue Apple Cafe. Employee meal discount during working hours is provided. Duties include food Read more
Cub Foods - *Apple* Valley - Now Hiring Par...
Cub Foods - Apple Valley - Now Hiring Part Time! United States of America, Minnesota, Apple Valley New Retail Post Date 4 days ago Requisition # 122305 Sign Up Read more
Cub Foods - *Apple* Valley - Now Hiring Par...
Cub Foods - Apple Valley - Now Hiring Part Time! United States of America, Minnesota, Apple Valley New Retail Post Date 3 days ago Requisition # 122305 Sign Up Read more
Executive Team Leader GM Sales (Assistant Man...
…(Assistant Manager General Merchandise and Operations) - Apple Valley, CaliforniaApply NowJob ID:R0000082364job family:Store Managementschedule:Full Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.