331 lines
14 KiB
Markdown
331 lines
14 KiB
Markdown
---
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title: Michael Abrash's Graphics Programming Black Book, Special Edition
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author: Michael Abrash
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date: '1997-07-01'
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isbn: '1576101746'
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publisher: The Coriolis Group
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category: 'Web and Software Development: Game Development,Web and Software Development:
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Graphics and Multimedia Development'
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chapter: '38'
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pages: 712-717
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---
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#### How Do You Fit Polygons Together? {#Heading5}
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How, then, do you fit polygons together? *Very* carefully. First, the
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line-tracing algorithm must be adjusted so that it selects only those
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pixels that are truly inside the polygon. This basically requires
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shifting a standard line-drawing algorithm horizontally by one
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half-pixel toward the polygon's interior. That leaves the issue of how
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to handle points that are exactly on the boundary, and points that lie
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at vertices, so that those points are drawn once and only once. To deal
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with that, we're going to adopt the following rules:
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* Points located exactly on nonhorizontal edges are drawn only if the
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interior of the polygon is directly to the right (left edges are
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drawn, right edges aren't).
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* Points located exactly on horizontal edges are drawn only if the
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interior of the polygon is directly below them (horizontal top edges
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are drawn, horizontal bottom edges aren't).
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* A vertex is drawn only if all lines ending at that point meet the
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above conditions (no right or bottom edges end at that point).
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All edges of a polygon except those that are flat tops or flat bottoms
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will be considered either right edges or left edges, regardless of
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slope. The left edge is the one that starts with the leftmost line down
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from the top of the polygon.
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These rules ensure that no pixel is drawn more than once when adjacent
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polygons are filled, and that if polygons cover the full 360-degree
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range around a pixel, then that pixel will be drawn once and only
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once—just what we need in order to be able to fit filled polygons
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together seamlessly.
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> 
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> This sort of non-overlapping polygon filling isn't ideal for all
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> purposes. Polygons are skewed toward the top and left edges, which not
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> only introduces drawing error relative to the ideal polygon but also
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> means that a filled polygon won't match the same polygon drawn unfilled.
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> Narrow wedges and one-pixel-wide polygons will show up spottily. All in
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> all, the choice of polygon-filling approach depends entirely on the ways
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> in which the filled polygons must be used.
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For our purposes, nonoverlapping polygons are the way to go, so let's
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have at them.
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### Filling Non-Overlapping Convex Polygons {#Heading6}
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Without further ado, Listing 38.1 contains a function,
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`FillConvexPolygon`, that accepts a list of points that describe a
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convex polygon, with the last point assumed to connect to the first, and
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scans it into a list of lines to fill, then passes that list to the
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function `DrawHorizontalLineList` in Listing 38.2. Listing 38.3 is a
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sample program that calls `FillConvexPolygon` to draw polygons of
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various sorts, and Listing 38.4 is a header file included by the other
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listings. Here are the listings; we'll pick up discussion on the other
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side.
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**LISTING 38.1 L38-1.C**
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```c
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/* Color-fills a convex polygon. All vertices are offset by (XOffset,
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YOffset). "Convex" means that every horizontal line drawn through
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the polygon at any point would cross exactly two active edges
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(neither horizontal lines nor zero-length edges count as active
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edges; both are acceptable anywhere in the polygon), and that the
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right & left edges never cross. (It's OK for them to touch, though,
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so long as the right edge never crosses over to the left of the
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left edge.) Nonconvex polygons won't be drawn properly. Returns 1
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for success, 0 if memory allocation failed. */
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#include <stdio.h>
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#include <math.h>
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#ifdef __TURBOC__
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#include <alloc.h>
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#else /* MSC */
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#include <malloc.h>
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#endif
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#include "polygon.h"
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/* Advances the index by one vertex forward through the vertex list,
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wrapping at the end of the list */
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#define INDEX_FORWARD(Index) \
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Index = (Index + 1) % VertexList->Length;
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/* Advances the index by one vertex backward through the vertex list,
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wrapping at the start of the list */
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#define INDEX_BACKWARD(Index) \
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Index = (Index - 1 + VertexList->Length) % VertexList->Length;
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/* Advances the index by one vertex either forward or backward through
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the vertex list, wrapping at either end of the list */
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#define INDEX_MOVE(Index,Direction) \
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if (Direction > 0) \
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Index = (Index + 1) % VertexList->Length; \
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else \
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Index = (Index - 1 + VertexList->Length) % VertexList->Length;
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extern void DrawHorizontalLineList(struct HLineList *, int);
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static void ScanEdge(int, int, int, int, int, int, struct HLine **);
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int FillConvexPolygon(struct PointListHeader * VertexList, int Color,
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int XOffset, int YOffset)
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{
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int i, MinIndexL, MaxIndex, MinIndexR, SkipFirst, Temp;
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int MinPoint_Y, MaxPoint_Y, TopIsFlat, LeftEdgeDir;
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int NextIndex, CurrentIndex, PreviousIndex;
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int DeltaXN, DeltaYN, DeltaXP, DeltaYP;
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struct HLineList WorkingHLineList;
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struct HLine *EdgePointPtr;
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struct Point *VertexPtr;
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/* Point to the vertex list */
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VertexPtr = VertexList->PointPtr;
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/* Scan the list to find the top and bottom of the polygon */
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if (VertexList->Length == 0)
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return(1); /* reject null polygons */
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MaxPoint_Y = MinPoint_Y = VertexPtr[MinIndexL = MaxIndex = 0].Y;
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for (i = 1; i < VertexList->Length; i++) {
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if (VertexPtr[i].Y < MinPoint_Y)
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MinPoint_Y = VertexPtr[MinIndexL = i].Y; /* new top */
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else if (VertexPtr[i].Y > MaxPoint_Y)
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MaxPoint_Y = VertexPtr[MaxIndex = i].Y; /* new bottom */
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}
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if (MinPoint_Y == MaxPoint_Y)
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return(1); /* polygon is 0-height; avoid infinite loop below */
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/* Scan in ascending order to find the last top-edge point */
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MinIndexR = MinIndexL;
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while (VertexPtr[MinIndexR].Y == MinPoint_Y)
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INDEX_FORWARD(MinIndexR);
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INDEX_BACKWARD(MinIndexR); /* back up to last top-edge point */
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/* Now scan in descending order to find the first top-edge point */
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while (VertexPtr[MinIndexL].Y == MinPoint_Y)
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INDEX_BACKWARD(MinIndexL);
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INDEX_FORWARD(MinIndexL); /* back up to first top-edge point */
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/* Figure out which direction through the vertex list from the top
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vertex is the left edge and which is the right */
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LeftEdgeDir = -1; /* assume left edge runs down thru vertex list */
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if ((TopIsFlat = (VertexPtr[MinIndexL].X !=
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VertexPtr[MinIndexR].X) ? 1 : 0) == 1) {
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/* If the top is flat, just see which of the ends is leftmost */
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if (VertexPtr[MinIndexL].X > VertexPtr[MinIndexR].X) {
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LeftEdgeDir = 1; /* left edge runs up through vertex list */
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Temp = MinIndexL; /* swap the indices so MinIndexL */
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MinIndexL = MinIndexR; /* points to the start of the left */
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MinIndexR = Temp; /* edge, similarly for MinIndexR */
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}
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} else {
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/* Point to the downward end of the first line of each of the
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two edges down from the top */
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NextIndex = MinIndexR;
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INDEX_FORWARD(NextIndex);
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PreviousIndex = MinIndexL;
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INDEX_BACKWARD(PreviousIndex);
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/* Calculate X and Y lengths from the top vertex to the end of
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the first line down each edge; use those to compare slopes
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and see which line is leftmost */
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DeltaXN = VertexPtr[NextIndex].X - VertexPtr[MinIndexL].X;
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DeltaYN = VertexPtr[NextIndex].Y - VertexPtr[MinIndexL].Y;
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DeltaXP = VertexPtr[PreviousIndex].X - VertexPtr[MinIndexL].X;
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DeltaYP = VertexPtr[PreviousIndex].Y - VertexPtr[MinIndexL].Y;
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if (((long)DeltaXN * DeltaYP - (long)DeltaYN * DeltaXP) < 0L) {
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LeftEdgeDir = 1; /* left edge runs up through vertex list */
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Temp = MinIndexL; /* swap the indices so MinIndexL */
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MinIndexL = MinIndexR; /* points to the start of the left */
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MinIndexR = Temp; /* edge, similarly for MinIndexR */
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}
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}
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/* Set the # of scan lines in the polygon, skipping the bottom edge
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and also skipping the top vertex if the top isn't flat because
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in that case the top vertex has a right edge component, and set
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the top scan line to draw, which is likewise the second line of
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the polygon unless the top is flat */
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if ((WorkingHLineList.Length =
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MaxPoint_Y - MinPoint_Y - 1 + TopIsFlat) <= 0)
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return(1); /* there's nothing to draw, so we're done */
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WorkingHLineList.YStart = YOffset + MinPoint_Y + 1 - TopIsFlat;
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/* Get memory in which to store the line list we generate */
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if ((WorkingHLineList.HLinePtr =
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(struct HLine *) (malloc(sizeof(struct HLine) *
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WorkingHLineList.Length))) == NULL)
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return(0); /* couldn't get memory for the line list */
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/* Scan the left edge and store the boundary points in the list */
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/* Initial pointer for storing scan converted left-edge coords */
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EdgePointPtr = WorkingHLineList.HLinePtr;
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/* Start from the top of the left edge */
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PreviousIndex = CurrentIndex = MinIndexL;
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/* Skip the first point of the first line unless the top is flat;
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if the top isn't flat, the top vertex is exactly on a right
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edge and isn't drawn */
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SkipFirst = TopIsFlat ? 0 : 1;
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/* Scan convert each line in the left edge from top to bottom */
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do {
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INDEX_MOVE(CurrentIndex,LeftEdgeDir);
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ScanEdge(VertexPtr[PreviousIndex].X + XOffset,
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VertexPtr[PreviousIndex].Y,
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VertexPtr[CurrentIndex].X + XOffset,
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VertexPtr[CurrentIndex].Y, 1, SkipFirst, &EdgePointPtr);
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PreviousIndex = CurrentIndex;
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SkipFirst = 0; /* scan convert the first point from now on */
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} while (CurrentIndex != MaxIndex);
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/* Scan the right edge and store the boundary points in the list */
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EdgePointPtr = WorkingHLineList.HLinePtr;
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PreviousIndex = CurrentIndex = MinIndexR;
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SkipFirst = TopIsFlat ? 0 : 1;
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/* Scan convert the right edge, top to bottom. X coordinates are
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adjusted 1 to the left, effectively causing scan conversion of
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the nearest points to the left of but not exactly on the edge */
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do {
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INDEX_MOVE(CurrentIndex,-LeftEdgeDir);
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ScanEdge(VertexPtr[PreviousIndex].X + XOffset - 1,
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VertexPtr[PreviousIndex].Y,
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VertexPtr[CurrentIndex].X + XOffset - 1,
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VertexPtr[CurrentIndex].Y, 0, SkipFirst, &EdgePointPtr);
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PreviousIndex = CurrentIndex;
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SkipFirst = 0; /* scan convert the first point from now on */
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} while (CurrentIndex != MaxIndex);
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/* Draw the line list representing the scan converted polygon */
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DrawHorizontalLineList(&WorkingHLineList, Color);
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/* Release the line list's memory and we're successfully done */
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free(WorkingHLineList.HLinePtr);
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return(1);
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}
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/* Scan converts an edge from (X1,Y1) to (X2,Y2), not including the
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point at (X2,Y2). This avoids overlapping the end of one line with
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the start of the next, and causes the bottom scan line of the
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polygon not to be drawn. If SkipFirst != 0, the point at (X1,Y1)
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isn't drawn. For each scan line, the pixel closest to the scanned
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line without being to the left of the scanned line is chosen. */
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static void ScanEdge(int X1, int Y1, int X2, int Y2, int SetXStart,
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int SkipFirst, struct HLine **EdgePointPtr)
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{
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int Y, DeltaX, DeltaY;
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double InverseSlope;
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struct HLine *WorkingEdgePointPtr;
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/* Calculate X and Y lengths of the line and the inverse slope */
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DeltaX = X2 - X1;
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if ((DeltaY = Y2 - Y1) <= 0)
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return; /* guard against 0-length and horizontal edges */
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InverseSlope = (double)DeltaX / (double)DeltaY;
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/* Store the X coordinate of the pixel closest to but not to the
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left of the line for each Y coordinate between Y1 and Y2, not
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including Y2 and also not including Y1 if SkipFirst != 0 */
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WorkingEdgePointPtr = *EdgePointPtr; /* avoid double dereference */
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for (Y = Y1 + SkipFirst; Y < Y2; Y++, WorkingEdgePointPtr++) {
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/* Store the X coordinate in the appropriate edge list */
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if (SetXStart == 1)
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WorkingEdgePointPtr->XStart =
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X1 + (int)(ceil((Y-Y1) * InverseSlope));
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else
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WorkingEdgePointPtr->XEnd =
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X1 + (int)(ceil((Y-Y1) * InverseSlope));
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}
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*EdgePointPtr = WorkingEdgePointPtr; /* advance caller's ptr */
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}
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```
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**LISTING 38.2 L38-2.C**
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```c
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/* Draws all pixels in the list of horizontal lines passed in, in
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mode 13h, the VGA's 320x200 256-color mode. Uses a slow pixel-by-
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pixel approach, which does have the virtue of being easily ported
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to any environment. */
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#include <dos.h>
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#include "polygon.h"
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#define SCREEN_WIDTH 320
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#define SCREEN_SEGMENT 0xA000
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static void DrawPixel(int, int, int);
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void DrawHorizontalLineList(struct HLineList * HLineListPtr,
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int Color)
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{
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struct HLine *HLinePtr;
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int Y, X;
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/* Point to the XStart/XEnd descriptor for the first (top)
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horizontal line */
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HLinePtr = HLineListPtr->HLinePtr;
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/* Draw each horizontal line in turn, starting with the top one and
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advancing one line each time */
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for (Y = HLineListPtr->YStart; Y < (HLineListPtr->YStart +
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HLineListPtr->Length); Y++, HLinePtr++) {
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/* Draw each pixel in the current horizontal line in turn,
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starting with the leftmost one */
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for (X = HLinePtr->XStart; X <= HLinePtr->XEnd; X++)
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DrawPixel(X, Y, Color);
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}
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}
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/* Draws the pixel at (X, Y) in color Color in VGA mode 13h */
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static void DrawPixel(int X, int Y, int Color) {
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unsigned char far *ScreenPtr;
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#ifdef __TURBOC__
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ScreenPtr = MK_FP(SCREEN_SEGMENT, Y * SCREEN_WIDTH + X);
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#else /* MSC 5.0 */
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FP_SEG(ScreenPtr) = SCREEN_SEGMENT;
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FP_OFF(ScreenPtr) = Y * SCREEN_WIDTH + X;
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#endif
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*ScreenPtr = (unsigned char)Color;
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}
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```
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