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------------------------ --------------------------------- --------------------
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[Previous](51-05.html) [Table of Contents](index.html) [Next](52-01.html)
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------------------------ --------------------------------- --------------------
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**LISTING 51.5 POLYGON.H**
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/* POLYGON.H: Header file for polygon-filling code, also includes a number of
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useful items for 3D animation. */
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#define MAX_POLY_LENGTH 4 /* four vertices is the max per poly */
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#define SCREEN_WIDTH 320
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#define SCREEN_HEIGHT 240
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#define PAGE0_START_OFFSET 0
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#define PAGE1_START_OFFSET (((long)SCREEN_HEIGHT*SCREEN_WIDTH)/4)
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/* Ratio: distance from viewpoint to projection plane / width of projection
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plane. Defines the width of the field of view. Lower absolute values = wider
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fields of view; higher values = narrower. */
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#define PROJECTION_RATIO -2.0 /* negative because visible Z coordinates are negative */
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/* Draws the polygon described by the point list PointList in color Color with
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all vertices offset by (X,Y) */
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#define DRAW_POLYGON(PointList,NumPoints,Color,X,Y) \
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Polygon.Length = NumPoints; Polygon.PointPtr = PointList; \
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FillConvexPolygon(&Polygon, Color, X, Y);
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/* Describes a single 2D point */
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struct Point {
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int X; /* X coordinate */
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int Y; /* Y coordinate */
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};
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/* Describes a single 3D point in homogeneous coordinates */
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struct Point3 {
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double X; /* X coordinate */
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double Y; /* Y coordinate */
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double Z; /* Z coordinate */
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double W;
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};
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/* Describes a series of points (used to store a list of vertices that
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describe a polygon; each vertex is assumed to connect to the two adjacent
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vertices, and the last vertex is assumed to connect to the first) */
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struct PointListHeader {
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int Length; /* # of points */
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struct Point * PointPtr; /* pointer to list of points */
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};
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/* Describes beginning and ending X coordinates of a single horizontal line */
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struct HLine {
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int XStart; /* X coordinate of leftmost pixel in line */
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int XEnd; /* X coordinate of rightmost pixel in line */
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};
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/* Describes a Length-long series of horizontal lines, all assumed to be on
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contiguous scan lines starting at YStart and proceeding downward (describes
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a scan-converted polygon to low-level hardware-dependent drawing code) */
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struct HLineList {
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int Length; /* # of horizontal lines */
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int YStart; /* Y coordinate of topmost line */
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struct HLine * HLinePtr; /* pointer to list of horz lines */
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};
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struct Rect { int Left, Top, Right, Bottom; };
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/* Structure describing one face of an object (one polygon) */
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struct Face {
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int * VertNums; /* pointer to vertex ptrs */
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int NumVerts; /* # of vertices */
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int Color; /* polygon color */
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};
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/* Structure describing an object */
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struct Object {
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int NumVerts;
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struct Point3 * VertexList;
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struct Point3 * XformedVertexList;
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struct Point3 * ProjectedVertexList;
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struct Point * ScreenVertexList;
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int NumFaces;
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struct Face * FaceList;
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};
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extern void XformVec(double Xform[4][4], double * SourceVec, double * DestVec);
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extern void ConcatXforms(double SourceXform1[4][4],
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double SourceXform2[4][4], double DestXform[4][4]);
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extern void XformAndProjectPoly(double Xform[4][4],
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struct Point3 * Poly, int PolyLength, int Color);
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extern int FillConvexPolygon(struct PointListHeader *, int, int, int);
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extern void Set320x240Mode(void);
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extern void ShowPage(unsigned int StartOffset);
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extern void FillRectangleX(int StartX, int StartY, int EndX,
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int EndY, unsigned int PageBase, int Color);
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extern void XformAndProjectPoints(double Xform[4][4],struct Object * ObjectToXform);
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extern void DrawVisibleFaces(struct Object * ObjectToXform);
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extern void AppendRotationX(double XformToChange[4][4], double Angle);
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extern void AppendRotationY(double XformToChange[4][4], double Angle);
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extern void AppendRotationZ(double XformToChange[4][4], double Angle);
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extern int DisplayedPage, NonDisplayedPage;
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extern struct Rect EraseRect[];
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### A Note on Rounding Negative Numbers {#Heading6}
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In the previous chapter, I added 0.5 and truncated in order to round
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values from floating-point to integer format. Here, in Listing 51.2,
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I’ve switched to adding 0.5 and using the **floor()** function. For
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positive values, the two approaches are equivalent; for negative values,
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only the **floor()** approach works properly.
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### Object Representation {#Heading7}
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Each object consists of a list of vertices and a list of faces, with the
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vertices of each face defined by pointers into the vertex list; this
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allows each vertex to be transformed exactly once, even though several
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faces may share a single vertex. Each object contains the vertices not
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only in their original, untransformed state, but in three other forms as
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well: transformed to view space, transformed and projected to screen
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space, and converted to screen coordinates. Earlier, we saw that it can
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be convenient to store the screen coordinates within the object, so that
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if the object hasn’t moved with respect to the viewer, it can be redrawn
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without the need for recalculation, but why bother storing the view and
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screen space forms of the vertices as well?
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The screen space vertices are useful for some sorts of hidden surface
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removal. For example, to determine whether two polygons overlap as seen
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by the viewer, you must first know how they look to the viewer,
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accounting for perspective; screen space provides that information. (So
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do the final screen coordinates, but with less accuracy, and without any
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Z information.) The view space vertices are useful for collision and
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proximity detection; screen space can’t be used here, because objects
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are distorted by the perspective projection into screen space. World
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space would serve as well as view space for collision detection, but
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because it’s possible to transform directly from object space to view
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space with a single matrix, it’s often preferable to skip over world
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space. It’s not mandatory that vertices be stored for all these
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different spaces, but the coordinates in all those spaces have to be
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calculated as intermediate steps anyway, so we might as well keep them
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around for those occasions when they’re needed.
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------------------------ --------------------------------- --------------------
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[Previous](51-05.html) [Table of Contents](index.html) [Next](52-01.html)
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------------------------ --------------------------------- --------------------
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* * * * *
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Graphics Programming Black Book © 2001 Michael Abrash
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