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Hi all!

I am working to implement in Objective C a class QuadEdge based on Guibas and Stolfi’s data structure for a GIS spatial data class. I have some design questions. I hope some people can help me in figuring these out.

I have found 3 implementations. Here are the abreiviated headers:

-C :

typedef int edge_ref;

typedef struct { edge_ref next[4]; //Stores ONext, SymDNext, RotRNext, TorLNext void *data[4]; //Stores origin, destination, LeftFace, RightFace unsigned mark; } edge_struct;

/* Edge orientation operators: */

#define ROT(e) (((e)&0xfffffffcu)+(((e)+1)&3u)) #define SYM(e) (((e)&0xfffffffcu)+(((e)+2)&3u)) #define TOR(e) (((e)&0xfffffffcu)+(((e)+3)&3u))

-C++ :

class QuadEdge; class Edge { friend QuadEdge; private: int num; Edge *next; Point2d *data; };

class QuadEdge { private: Edge e[4]; };

inline Edge* Edge::Rot() //Return the dual of the current edge { return (num < 3) ? this + 1 : this - 3; }

inline Edge* Edge::Sym() { return (num < 2) ? this + 2 : this -2; }

inline Edge* Edge::invRot() { return (num > 0) ? this - 1 : this + 3; }

-Delphi : "The Quad-Arc Data Structure" by C Gold

TQuad = class N : TQuad; R : TQuad; V : TPoint; Index : Integer; end;

function TQuad.Rot : TQuad; begin Sym := Self.R; end;

function TQuad.Sym : TQuad; begin Sym := Self.R.R; end;

function TQuad.Inv : TQuad; begin Sym := Self.R.R.R; end;

The 3 use different approaches and I am trying to decide which approach to use to make a ObjectiveC class. I would like my QuadEdge class to have the following variables:

NSString* edgeId; Unique ID for each edge. NSString* lineId; Unique ID for each line composed of edges. id vertex; Refers to either a point or a face.

I have tried it using the following header based on the Delphi implementation:

@interface GISEdge : NSObject { NSString* lineId; NSString* edgeId; GISEdge* next; GISEdge* rotate; id vertex; BOOL internal; // Edge is inside the hull of the TIN (1) or on the edge is part of the outer hull (0) }

But this implementation seems to be way too bloated because each edge has 4 GISEdge structures. If a Voronoi diagram of any significant size uses this structure, it will be way too big, won’t it?

So back to the drawing board. I looked at the C++ implementation and started:

typedef struct edge Edge; struct edge { int num; Edge* next; id data; };

@interface GISEdge : NSObject { NSString* lineId; NSString* edgeId; Edge e[4]; }

But if next points to edge[2] of QuadEdge “PR102”, how can I get the edgeId for edge[2]? This seems too complicated. Yet I like the fact that the edgeId, lineId, and interior variables are only stored once and are associated where they should be, in the QuadEdge and not in the Edge. I could also add new items to the QuadEdge later without a 4x increase in size for every edge.

Another thought that has crossed my mind is to create a GISLayer class that hides individual edges. This would be more like the Symbol-Table Abstract Data Types I learned in Sedgewick’s Algorithms books.

This data structure is more advanced than anything I have done before. Any thoughts or suggestions are appreciated!


If it is already available as a C library then why do you want to go and re-implement it in Objective-C? I would simply write a couple of helper classes to wrap the entire library. RbrtPntn.