Polygons are the basic components of almost all 2D objects in the DR2D FORM. Lines, squares, circles, and arcs are all examples of DR2D polygons. There are two types of DR2D polygons, the open polygon (OPLY) and the closed polygon (CPLY). The difference between a closed and open polygon is that the computer adds a line segment connecting the endpoints of a closed polygon so that it is a continuous path. An open polygon's endpoints do not have to meet, like the endpoints of a line segment. struct POLYstruct { ULONG ID; ULONG Size; USHORT NumPoints; IEEE PolyPoints[2*NumPoints]; }; The NumPoints field contains the number of points in the polygon and the PolyPoints array contains the (X, Y) coordinates of the points of the non-curved parts of polygons. The even index elements are X coordinates and the odd index elements are Y coordinates. Figure 3 - Bezier curves DR2D uses Bezier cubic sections, or cubic splines, to describe curves in polygons. A set of four coordinates (P1 through P4) defines the shape of a cubic spline. The first coordinate (P1) is the point where the curve begins. The line from the first to the second coordinate (P1 to P2) is tangent to the curve at the first point. The line from P3 to P4 is tangent to the cubic section, where it ends at P4. The coordinates describing the cubic section are stored in the PolyPoints[] array with the coordinates of the normal points. DR2D inserts an indicator point before a set of cubic section points to differentiate a normal point from the points that describe a curve. An indicator point has an X value of 0xFFFFFFFF. The indicator point's Y value is a bit field. If this bit field's low-order bit is set, the points that follow the indicator point make up a cubic section. The second lowest order bit in the indicator point's bit field is the MOVETO flag. If this bit is set, the point (or set of cubic section points) starts a new polygon, or subpolygon. This subpolygon will appear to be completely separate from other polygons but there is an important connection between a polygon and its subpolygon. Subpolygons make it possible to create holes in polygons. An example of a polygon with a hole is the letter "O". The "O" is a filled circular polygon with a smaller circular polygon within it. The reason the inner polygon isn't covered up when the outer polygon is filled is that DR2D fills are done using the even-odd rule. The even-odd rule determines if a point is "inside" a polygon by drawing a ray outward from that point and counting the number of path segments the ray crosses. If the number is even, the point is outside the object and shouldn't be filled. Conversely, an odd number of crossings means the point is inside and should be filled. DR2D only applies the even-odd rule to a polygon and its subpolygons, so no other objects are considered in the calculations. Taliesin, Inc. supplied the following algorithm to illustrate the format of DR2D polygons. OPLYs, CPLYs, AROWs, and ProVector's outline fonts all use the same format: typedef union { IEEE num; LONG bits; } Coord; #define INDICATOR 0xFFFFFFFF #define IND_SPLINE 0x00000001 #define IND_MOVETO 0x00000002 /* A common pitfall in attempts to support DR2D has been to fail to recognize the case when an INDICATOR point indicates the following coordinate to be the first point of BOTH a Bezier cubic and a sub-polygon, ie. the value of the flag = (IND_CURVE | IND_MOVETO) */ Coord Temp0, Temp1; int FirstPoint, i, Increment; /* Initialize the path */ NewPath(); FirstPoint = 1; /* Draw the path */ i = 0; while( i < NumPoints ) { Temp0.num = PolyPoints[2*i]; Temp1.num = PolyPoints[2*i + 1]; if( Temp0.bits == INDICATOR ) { /* Increment past the indicator */ Increment = 1; if( Temp1.bits & IND_MOVETO ) { /* Close and fill, if appropriate */ if( ID == CPLY ) { FillPath(); } else { StrokePath(); } /* Set up the new path */ NewPath(); FirstPoint = 1; } if( Temp1.bits & IND_CURVE ) { /* The next 4 points are Bezier cubic control points */ if( FirstPoint ) MoveTo( PolyPoints[2*i + 2], PolyPoints[2*i + 3] ); else LineTo( PolyPoints[2*i + 2], PolyPoints[2*i + 3] ); CurveTo( PolyPoints[2*i + 4], PolyPoints[2*i + 5], PolyPoints[2*i + 6], PolyPoints[2*i + 7], PolyPoints[2*i + 8], PolyPoints[2*i + 9] ); FirstPoint = 0; /* Increment past the control points */ Increment += 4; } } else { if( FirstPoint ) MoveTo( PolyPoints[2*i], PolyPoints[2*i + 1] ); else LineTo( PolyPoints[2*i], PolyPoints[2*i + 1] ); FirstPoint = 0; /* Increment past the last endpoint */ Increment = 1; } /* Add the increment */ i += Increment; } /* Close the last path */ if( ID == CPLY ) { FillPath(); } else { StrokePath(); }

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