/* * Copyright © 2002 University of Southern California * * Permission to use, copy, modify, distribute, and sell this software * and its documentation for any purpose is hereby granted without * fee, provided that the above copyright notice appear in all copies * and that both that copyright notice and this permission notice * appear in supporting documentation, and that the name of University * of Southern California not be used in advertising or publicity * pertaining to distribution of the software without specific, * written prior permission. University of Southern California makes * no representations about the suitability of this software for any * purpose. It is provided "as is" without express or implied * warranty. * * UNIVERSITY OF SOUTHERN CALIFORNIA DISCLAIMS ALL WARRANTIES WITH * REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF * MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL UNIVERSITY OF * SOUTHERN CALIFORNIA BE LIABLE FOR ANY SPECIAL, INDIRECT OR * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS * OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. * * Author: Carl Worth, USC, Information Sciences Institute */ #include "icint.h" #define MIN(a,b) ((a) < (b) ? (a) : (b)) #define MAX(a,b) ((a) > (b) ? (a) : (b)) IcImage * IcCreateAlphaPicture (IcImage *dst, IcFormat *format, uint16_t width, uint16_t height) { IcImage *image; int own_format = 0; if (width > 32767 || height > 32767) return 0; if (!format) { own_format = 1; if (dst->polyEdge == PolyEdgeSharp) format = IcFormatCreate (IcFormatNameA1); else format = IcFormatCreate (IcFormatNameA8); if (!format) return 0; } image = IcImageCreate (format, width, height); if (own_format) IcFormatDestroy (format); /* XXX: Is this a reasonable way to clear the image? Would probably be preferable to use IcImageFillRectangle once such a beast exists. */ memset (image->pixels->data, 0, height * image->pixels->stride); return image; } static IcFixed16_16 IcLineFixedX (const IcLineFixed *l, IcFixed16_16 y, int ceil) { IcFixed16_16 dx = l->p2.x - l->p1.x; xFixed_32_32 ex = (xFixed_32_32) (y - l->p1.y) * dx; IcFixed16_16 dy = l->p2.y - l->p1.y; if (ceil) ex += (dy - 1); return l->p1.x + (IcFixed16_16) (ex / dy); } static void IcTrapezoidBounds (int ntrap, const IcTrapezoid *traps, PixRegionBox *box) { box->y1 = MAXSHORT; box->y2 = MINSHORT; box->x1 = MAXSHORT; box->x2 = MINSHORT; for (; ntrap; ntrap--, traps++) { int16_t x1, y1, x2, y2; if (!xTrapezoidValid(traps)) continue; y1 = xFixedToInt (traps->top); if (y1 < box->y1) box->y1 = y1; y2 = xFixedToInt (xFixedCeil (traps->bottom)); if (y2 > box->y2) box->y2 = y2; x1 = xFixedToInt (MIN (IcLineFixedX (&traps->left, traps->top, 0), IcLineFixedX (&traps->left, traps->bottom, 0))); if (x1 < box->x1) box->x1 = x1; x2 = xFixedToInt (xFixedCeil (MAX (IcLineFixedX (&traps->right, traps->top, 1), IcLineFixedX (&traps->right, traps->bottom, 1)))); if (x2 > box->x2) box->x2 = x2; } } void IcCompositeTrapezoids (IcOperator op, IcImage *src, IcImage *dst, int xSrc, int ySrc, const IcTrapezoid *traps, int ntraps) { IcImage *image = NULL; PixRegionBox bounds; int16_t xDst, yDst; int16_t xRel, yRel; IcFormat *format; if (ntraps == 0) return; xDst = traps[0].left.p1.x >> 16; yDst = traps[0].left.p1.y >> 16; format = IcFormatCreate (IcFormatNameA8); if (format) { IcTrapezoidBounds (ntraps, traps, &bounds); if (bounds.y1 >= bounds.y2 || bounds.x1 >= bounds.x2) return; image = IcCreateAlphaPicture (dst, format, bounds.x2 - bounds.x1, bounds.y2 - bounds.y1); if (!image) return; } for (; ntraps; ntraps--, traps++) { if (!xTrapezoidValid(traps)) continue; if (!format) { IcTrapezoidBounds (1, traps, &bounds); if (bounds.y1 >= bounds.y2 || bounds.x1 >= bounds.x2) continue; image = IcCreateAlphaPicture (dst, format, bounds.x2 - bounds.x1, bounds.y2 - bounds.y1); if (!image) continue; } IcRasterizeTrapezoid (image, traps, -bounds.x1, -bounds.y1); if (!format) { xRel = bounds.x1 + xSrc - xDst; yRel = bounds.y1 + ySrc - yDst; IcComposite (op, src, image, dst, xRel, yRel, 0, 0, bounds.x1, bounds.y1, bounds.x2 - bounds.x1, bounds.y2 - bounds.y1); IcImageDestroy (image); } } if (format) { xRel = bounds.x1 + xSrc - xDst; yRel = bounds.y1 + ySrc - yDst; IcComposite (op, src, image, dst, xRel, yRel, 0, 0, bounds.x1, bounds.y1, bounds.x2 - bounds.x1, bounds.y2 - bounds.y1); IcImageDestroy (image); } IcFormatDestroy (format); } #ifdef DEBUG #include #include #define ASSERT(e) assert(e) #endif #ifndef ASSERT #define ASSERT(e) #endif #ifndef MAX #define MAX(a, b) ((a) > (b) ? (a) : (b)) #endif #ifndef MIN #define ICN(a, b) ((a) < (b) ? (a) : (b)) #endif #define MAX_AREA 0x80000000 /* * A RationalPoint is an exact position along one of the trapezoid * edges represented by an approximate position (x,y) and two error * terms (ex_dy, ey_dx). The error in X is multiplied by the Y * dimension of the line while the error in Y is multiplied by the * X dimension of the line, allowing an exact measurement of the * distance from (x,y) to the line. * * Generally, while walking an edge, one of ex_dy/ey_dx will be zero * indicating that the position error is held in the other. */ typedef struct { xFixed x; xFixed ex_dy; xFixed y; xFixed ey_dx; } RationalPoint; /* * Edges are walked both horizontally and vertically * They are walked vertically to get to a particular row * of pixels, and then walked horizontally within that row * to compute pixel coverage. * * Edges are always walked from top to bottom and from * left to right. This means that for lines moving leftwards * from top to bottom, the left to right walking actually moves * backwards along the line with respect to the top to bottom * walking. */ /* * A RationalRow represents the two positions where an * edge intersects a row of the trapezoid. Either or * both points may be on sub-pixel boundaries when at * the top or bottom of the trapezoid. This is used to * walk an edge vertically. */ typedef struct { RationalPoint top; /* intersection at top of row */ RationalPoint bottom; /* intersection at bottom of row */ } RationalRow; /* * A RationalCol represents the two positions where an * edge intersects a column of pixels. Both left and * right are always on whole pixel boundaries. */ typedef struct { RationalPoint left; /* intersection at left of column */ RationalPoint right; /* intersection at right of column */ } RationalCol; /* Here are some thoughts on line walking: Conditions: c2.x - c1.x = 1 r2.y - r1.y = 1 A B C D E F G H c1\ c1 c2 /c2 r1 r1 |\ \ r1 r1 / r1/| r1 r1 \-+---+ \-+---+ +-\-+ +\--+ +--/+ +-/-+ +---+-/ +---+-/ \| | `.c1 | |r1\| | \ | | / | |/ | | .' | |/ c1\ | |`-.|c2 | \c2 | | | | | | c1/ | c1|,_/|c2 | /c2 |\ | | `. | |\ | \ | | / | /| | ./ | | /| +-\-+ +---+-\ +---+-\ +--\+ +/--+ /-+---+ /-+---+ +-/-+ r2\| r2 r2 r2\ /r2 r2 r2 |/r2 \c2 c2 c1 c1/ Bottom Right Right Bottom Top Top Right Right State transitions: A -> C, D E -> E, F B -> A, B F -> G, H C -> A, B G -> G, H D -> C, D H -> E, F */ /* * Values for PixelWalk.depart. Top and Bottom can have the same value * as only one mode is possible given a line of either positive or * negative slope. These mark the departure edge while walking * rightwards across columns. */ typedef enum _departure { DepartTop = 0, /* edge exits top of pixel */ DepartBottom = 0, /* edge exits bottom of pixel */ DepartRight = 1 /* edge exits right edge of pixel */ } Departure; /* * PixelWalk * * This structure holds state to walk a single edge down the trapezoid. * * The edge is walked twice -- once by rows and once by columns. * The two intersections of the pixel by the edge are then set * from either the row or column position, depending on which edge * is intersected. * * Note that for lines moving left, walking by rows moves down the * line (increasing y) while walking by columns moves up the line * (decreasing y). */ typedef struct { xFixed dx; xFixed ey_thresh; xFixed dy; xFixed ex_thresh; Departure depart; /* slope */ xFixed m; xFixed em_dx; xFixed y_correct; xFixed ey_correct; /* Inverse slope. Does this have a standard symbol? */ xFixed p; xFixed ep_dy; xFixed x_correct; xFixed ex_correct; /* * Current edge positions along pixel rows and columns */ RationalRow row; RationalCol col; /* * The two intersections with the current pixel. * These are copied from either row or col as appropriate. */ RationalPoint upper; RationalPoint lower; } PixelWalk; #if 0 #ifdef GCC #define INLINE inline #endif #endif #ifndef INLINE #define INLINE #endif /* * Set a RationalPoint to an exact sub-pixel coordinate */ static void rationalPointInit (RationalPoint *pt, xFixed x, xFixed y) { pt->x = x; pt->ex_dy = 0; pt->y = y; pt->ey_dx = 0; } /* Calculate a / b, rounding down to the nearest integer */ static xFixed DivFloor(xFixed_32_32 a, xFixed b) { xFixed q; /* C allows implementation-defined rounding when using / with negative integers. Force all arguments to be positive to guarantee consistency. */ int neg = (a < 0 != b < 0); if (a < 0) a = -a; if (b < 0) b = -b; q = a / b; if (neg) q = -q; return q; } /* * Step 'pt' vertically to 'newy'. */ static INLINE void pixelWalkMovePointToY (PixelWalk *pw, RationalPoint *pt, xFixed newy) { xFixed_32_32 oex; xFixed xoff; /* X error of old X position and new Y position */ oex = (xFixed_32_32) pw->dx * (newy - pt->y) - pt->ey_dx + pt->ex_dy; /* amount to step X by */ xoff = DivFloor(oex, pw->dy); /* step X */ pt->x = pt->x + xoff; /* set new X error value for new X position and new Y positition */ pt->ex_dy = oex - (xFixed_32_32) pw->dy * xoff; /* Ensure that pt->x is always rounded down from the true X position, (ie. pt->ex_dy must be positive) */ if (pt->ex_dy < 0) { pt->x--; pt->ex_dy += pw->dy; } /* set new Y position, set Y error to zero */ pt->y = newy; pt->ey_dx = 0; } /* * Step 'pt' horizontally to 'newx' */ static INLINE void pixelWalkMovePointToX (PixelWalk *pw, RationalPoint *pt, xFixed newx) { xFixed_32_32 oey; xFixed yoff; /* Special case vertical lines to arbitrary y */ if (pw->dx == 0) { pt->x = newx; pt->ex_dy = 0; pt->y = 0; pt->ey_dx = 0; } else { /* Y error of old Y position and new X position */ oey = (xFixed_32_32) pw->dy * (newx - pt->x) - pt->ex_dy + pt->ey_dx; /* amount to step Y by */ yoff = DivFloor(oey, pw->dx); /* step Y */ pt->y = pt->y + yoff; /* set new Y error value for new Y position and new X position */ pt->ey_dx = oey - (xFixed_32_32) pw->dx * yoff; /* Ensure that pt->y is always rounded down from the true Y position, (ie. pt->ey_dx/pw->dx must be positive) */ if ((pw->dx > 0 && pt->ey_dx < 0) || (pw->dx < 0 && pt->ey_dx > 0)) { pt->y--; pt->ey_dx += pw->dx; } /* set new X position, set X error to zero */ pt->x = newx; pt->ex_dy = 0; } } /* * Step the 'row' element of 'pw' vertically (increasing y) to the * next y coordinate, (either the next full pixel value or the bottom * of the trapezoid, whichever comes first). */ static INLINE void pixelWalkStepRow (PixelWalk *pw) { /* pw.row.top.y < pw.row.bottom.y */ /* * Copy the current bottom point into the top point */ pw->row.top = pw->row.bottom; /* * Now incrementally walk bottom to the next column intersection */ pw->row.bottom.y += xFixed1; pw->row.bottom.x += pw->p; pw->row.bottom.ex_dy += pw->ep_dy; if ((pw->row.bottom.ex_dy > pw->ex_thresh) || ((pw->dx < 0) && (pw->row.bottom.ex_dy < 0))) { pw->row.bottom.x += pw->x_correct; pw->row.bottom.ex_dy += pw->ex_correct; } } /* * Step the 'col' element of 'pw' horizontally * (increasing x) by one whole pixel */ static INLINE void pixelWalkStepCol (PixelWalk *pw) { /* pw.col.p1.x < pw.col.p2.x */ /* * Copy the current right point into the left point */ pw->col.left = pw->col.right; /* * Now incrementally walk right to the next column intersection */ pw->col.right.x += xFixed1; pw->col.right.y += pw->m; pw->col.right.ey_dx += pw->em_dx; if ((pw->col.right.ey_dx > pw->ey_thresh) || ((pw->dx < 0) && (pw->col.right.ey_dx > 0))) { pw->col.right.y += pw->y_correct; pw->col.right.ey_dx += pw->ey_correct; } } /* * Walk to the nearest edge of the next pixel, filling in both p1 and * p2 as necessary from either the row or col intersections. * * The "next" pixel is defined to be the next pixel intersected by the * line with pixels visited in raster scan order, (for the benefit of * cache performance). For lines with positive slope it is easy to * achieve raster scan order by simply calling StepCol for each pixel * in a given scanline, then calling StepRow once at the end of each * scanline. * * However, for lines of negative slope where the magnitude of dx is * greater than dy, a little more work needs to be done. The pixels of * a particular scanline will be visited by succesive calls to StepCol * as before. This will effectively step "up" the line as we scan from * left to right. But, the call to StepRow at the end of the scan line * will step "down" the line and the column information will be * invalid at that point. * * For now, I fix up the column of all negative slope lines by calling * MovePointToX at the end of each scanline. However, this is an * extremely expensive operation since it involves a 64-bit multiply * and a 64-bit divide. It would be much better, (at least as long as * abs(dx) is not much greater than dy), to instead step the col * backwards as many times as necessary. */ static INLINE void pixelWalkNextPixel (PixelWalk *pw) { if (pw->dx < 0) { /* * left moving lines * * Check which pixel edge we're departing from * * Remember that in this case (dx < 0), the 'row' element of 'pw' * walks down the line while 'col' walks up */ if (pw->depart == DepartTop) { /* * The edge departs the row at this pixel, the * next time it gets used will be for the next row * * Step down one row and then recompute the * column values to start the next row of * pixels */ pixelWalkStepRow(pw); /* * Set column exit pixel */ pixelWalkMovePointToX(pw, &pw->col.right, xFixedFloor(pw->row.bottom.x)); /* * This moves the exit pixel to the entry pixel * and computes the next exit pixel */ pixelWalkStepCol(pw); /* * The first pixel on the next row will always * be entered from below, set the lower * intersection of this edge with that pixel */ pw->lower = pw->row.bottom; } else /* pw->depart == DepartRight */ { /* * easy case -- just move right one pixel */ pixelWalkStepCol(pw); /* * Set the lower intersection of the edge with the * pixel -- that's just where the edge entered * the pixel from the left */ pw->lower = pw->col.left; } /* * Now compute which edge the pixel * is departing from */ if (pw->row.top.x <= pw->col.right.x) { /* * row intersection is left of column intersection, * that means the edge hits the top of the pixel * before it hits the right edge */ pw->upper = pw->row.top; pw->depart = DepartTop; } else { /* * Row intersection is right of colum intersection, * that means the edge hits the right edge of the * pixel first */ pw->upper = pw->col.right; pw->depart = DepartRight; } } else { /* * right moving lines * * Check which edge we're departing from * * In the dx >= 0 case, the row and col elements both * walk downwards */ if (pw->depart == DepartBottom) { /* * The edge departs the row at this pixel, * the next time it gets used will be for the * next row * * Step down one row and (maybe) over one * column to prepare for the next row */ if (pw->row.bottom.x == pw->col.right.x) { /* * right through the corner of the pixel, * adjust the column */ pixelWalkStepCol(pw); } pixelWalkStepRow(pw); /* * Set the upper intersection of the edge with * the pixel, the first pixel on the next * row is always entered from the top */ pw->upper = pw->row.top; } else /* pw->depart == DepartRight */ { /* * Easy case -- move right one * pixel */ pixelWalkStepCol(pw); /* * Set the upper intersection of the edge * with the pixel, that's along the left * edge of the pixel */ pw->upper = pw->col.left; } /* * Now compute the exit edge and the * lower intersection of the edge with the pixel */ if (pw->row.bottom.x <= pw->col.right.x) { /* * Hit the place where the edge leaves * the pixel, the lower intersection is * where the edge hits the bottom */ pw->lower = pw->row.bottom; pw->depart = DepartBottom; } else { /* * The edge goes through the * next pixel on the row, * the lower intersection is where the * edge hits the right side of the pixel */ pw->lower = pw->col.right; pw->depart = DepartRight; } } } /* * Compute the first pixel intersection points * and the departure type from that pixel */ static void pixelWalkFirstPixel (PixelWalk *pw) { if (pw->dx < 0) { if (pw->row.top.x <= pw->col.right.x) { /* * leaving through the top. * upper position is the upper point of * the 'row' element */ pw->depart = DepartTop; pw->upper = pw->row.top; } else { /* * leaving through the right side * upper position is the right point of * the 'col' element */ pw->depart = DepartRight; pw->upper = pw->col.right; } /* * Now find the lower pixel intersection point */ if (pw->row.bottom.x >= pw->col.left.x) /* * entering through bottom, * lower position is the bottom point of * the 'row' element */ pw->lower = pw->row.bottom; else /* * entering through left side, * lower position is the left point of * the 'col' element */ pw->lower = pw->col.left; } else { if (pw->row.bottom.x <= pw->col.right.x) { /* * leaving through the bottom (or corner). * lower position is the lower point of * the 'row' element */ pw->depart = DepartBottom; pw->lower = pw->row.bottom; } else { /* * leaving through the right side * lower position is the right point of * the 'col' element */ pw->depart = DepartRight; pw->lower = pw->col.right; } /* * Now find the upper pixel intersection point */ if (pw->row.top.x >= pw->col.left.x) { /* * entering through the top (or corner), * upper position is the top point * of the 'row' element */ pw->upper = pw->row.top; } else { /* * entering through the left side, * upper position is the left point of * the 'col' element */ pw->upper = pw->col.left; } } } static void pixelWalkInit (PixelWalk *pw, IcLineFixed *line, IcFixed16_16 top_y, IcFixed16_16 bottom_y) { xFixed_32_32 dy_inc, dx_inc; IcPointFixed *top, *bot; /* * Orient lines top down */ if (line->p1.y < line->p2.y) { top = &line->p1; bot = &line->p2; } else { top = &line->p2; bot = &line->p1; } pw->dx = bot->x - top->x; pw->dy = bot->y - top->y; /* * Set step values for walking lines. * * These values are constructed so that the approximations in line * position will always be rounded down from the ideal position. */ pw->ex_thresh = pw->dy; pw->ey_thresh = abs(pw->dx); if (pw->dx < 0) { pw->x_correct = -1; pw->ex_correct = pw->dy; pw->y_correct = -1; pw->ey_correct = pw->dx; } else { pw->x_correct = 1; pw->ex_correct = -pw->dy; pw->y_correct = 1; pw->ey_correct = -pw->dx; } /* * Compute Bresenham values for walking edges incrementally */ dy_inc = (xFixed_32_32) xFixed1 * pw->dy; /* > 0 */ if (pw->dx != 0) { pw->m = dy_inc / pw->dx; /* sign(dx) */ pw->em_dx = dy_inc - (xFixed_32_32) pw->m * pw->dx; /* < 0 or > 0 */ } else { /* Vertical line. Setting these to zero prevents us from having to put any conditions in pixelWalkStepCol. */ pw->m = 0; pw->em_dx = 0; } dx_inc = (xFixed_32_32) xFixed1 * (xFixed_32_32) pw->dx; /* sign(dx) */ pw->p = dx_inc / pw->dy; /* sign(dx) */ pw->ep_dy = dx_inc - (xFixed_32_32) pw->p * pw->dy; /* < 0 or > 0 */ /* * row.bottom must be on the line before it can move. */ rationalPointInit(&pw->row.bottom, top->x, top->y); /* * Move row to the first scanline of the trapezoid. Do this by * first moving 'bottom' to the top of the trapezoid, and then * calling StepRow which copies that point to 'top' and computes * the next 'bottom'. */ pixelWalkMovePointToY(pw, &pw->row.bottom, xFixedFloor(top_y)); pixelWalkStepRow(pw); /* * col.right must be on the line before it can move. */ rationalPointInit(&pw->col.right, top->x, top->y); /* * Move col to the left-most pixel of the trapezoid in the first * scanline. Do this by first setting 'right' based on the * left-most endpoint of row, and then using StepCol which copies * that point to 'left' and computes the next 'right'. */ pixelWalkMovePointToX(pw, &pw->col.right, xFixedFloor(MIN(pw->row.top.x, pw->row.bottom.x))); pixelWalkStepCol(pw); /* * Compute first pixel intersections and the * first departure state */ pixelWalkFirstPixel (pw); } #define RoundShift(a,b) (((a) + (1 << ((b) - 1))) >> (b)) #define MaxAlpha(depth) ((1 << (depth)) - 1) #define AreaAlpha(area, depth) (RoundShift (RoundShift (area, depth) * \ MaxAlpha (depth), \ (31 - depth))) /* Pixel coverage from the upper-left corner bounded by one horizontal bottom line (bottom) and one line defined by two points, (x1,y1) and (x2,y2), which intersect the pixel. y1 must be less than y2. There are 8 cases yielding the following area calculations: A B C D E F G H +---+ +---+ +-1-+ +1--+ +--1+ +-1-+ +---+ +---+ | | 1 | | \| | \ | | / | |/ | | 1 | | 1 | |`-.| | 2 | | | | | | 2 | |,_/| | 1 |\ | | 2 | | | \ | | / | | | 2 | | /| +-2-+ +---+ +---+ +--2+ +2--+ +---+ +---+ +-2-+ A: (1/2 * x2 * (y2 - y1)) B: (1/2 * x2 * (y2 - y1)) + (bottom - y2) * x2 C: (1/2 * (x1 + x2) * y2 ) + (bottom - y2) * x2 D: (1/2 * (x1 + x2) * y2 ) E: (1/2 * (x1 + x2) * y2 ) F: (1/2 * x1 * y2 ) G: (1/2 * x1 * (y2 - y1)) + x1 * y1 H: (1/2 * (x1 + x2) * (y2 - y1)) + x1 * y1 The union of these calculations is valid for all cases. Namely: (1/2 * (x1 + x2) * (y2 - y1)) + (bottom - y2) * x2 + x1 * y1 An exercise for later would perhaps be to optimize the calculations for some of the cases above. Specifically, it's possible to eliminate multiplications by zero in several cases, leaving a maximum of two multiplies per pixel calculation. (This is even more promising now that the higher level code actually computes the exact same 8 cases as part of its pixel walking). But, for now, I just want to get something working correctly even if slower. So, we'll use the non-optimized general equation. */ /* 1.16 * 1.16 -> 1.31 */ #define AREA_MULT(w, h) ( (xFixed_1_31) (((((xFixed_1_16)w)*((xFixed_1_16)h) + 1) >> 1) | (((xFixed_1_16)w)&((xFixed_1_16)h)&0x10000) << 15)) /* (1.16 + 1.16) / 2 -> 1.16 */ #define WIDTH_AVG(x1,x2) (((x1) + (x2) + 1) >> 1) /* #define AreaAboveLeft(bottom, x1, y1, x2, y2) \ (xFixed_1_31) ( \ AREA_MULT((x1), (y1)) \ + AREA_MULT(WIDTH_AVG((x1), (x2)), (y2) - (y1))\ + AREA_MULT((x2), (bottom) - (y2)) \ ) */ static xFixed_1_31 AreaAboveLeft(xFixed_1_16 bottom, xFixed_1_16 x1, xFixed_1_16 y1, xFixed_1_16 x2, xFixed_1_16 y2) { xFixed_1_16 x_trap; xFixed_1_16 h_top, h_trap, h_bot; xFixed_1_31 area; x_trap = WIDTH_AVG(x1,x2); h_top = y1; h_trap = (y2 - y1); h_bot = (bottom - y2); area = AREA_MULT(x1, h_top) + AREA_MULT(x_trap, h_trap) + AREA_MULT(x2, h_bot); return area; } #define AlphaAboveLeft(bottom, x1, y1, x2, y2, depth) \ ( \ AreaAlpha( \ AreaAboveLeft((bottom), (x1), (y1), (x2), (y2)), \ (depth) \ ) \ ) /* static int AlphaAboveLeft(xFixed_1_16 bottom, xFixed_1_16 x1, xFixed_1_16 y1, xFixed_1_16 x2, xFixed_1_16 y2, int depth) { xFixed_1_31 area; area = AreaAboveLeft(bottom, x1, y1, x2, y2); return AreaAlpha(area, depth); } */ /* Alpha of a pixel above a given horizontal line */ #define AlphaAbove(pixel_y, line_y, depth) \ ( \ AreaAlpha(AREA_MULT((line_y) - (pixel_y), xFixed1), depth) \ ) static int RectAlpha(xFixed pixel_y, xFixed top, xFixed bottom, int depth) { if (depth == 1) return top == pixel_y ? 1 : 0; else { return AlphaAbove (pixel_y, bottom, depth) - AlphaAbove (pixel_y, top, depth); } } /* Pixel coverage from the left edge bounded by two horizontal lines, (top and bottom), as well as one line two points, p1 and p2, which intersect the pixel. The following condition must be true: p2.y > p1.y */ /* lr |\ +--|-\-------+ | a| b\ | =======|===\========== top | c| d \ =======|=====\======== bot | | \ | +--|-------\-+ alpha(d) = alpha(cd) - alpha(c) = alpha(abcd) - alpha(ab) - (alpha(ac) - alpha(a)) alpha(d) = pixel_alpha(top, bot, right) - pixel_alpha(top, bot, left) pixel_alpha(top, bot, line) = alpha_above_left(bot, line) - alpha_above_left(top, line) */ static int PixelAlpha(xFixed pixel_x, xFixed pixel_y, xFixed top, xFixed bottom, PixelWalk *pw, int depth) { int alpha; /* * Sharp polygons are different, alpha is 1 if the * area includes the pixel origin, else zero, in * the above figure, only 'a' has alpha 1 */ if (depth == 1) { alpha = 0; if (top == pixel_y && pw->upper.x != pixel_x) alpha = 1; } else { RationalPoint upper = pw->upper; RationalPoint lower = pw->lower; int bottom_alpha, top_alpha; bottom_alpha = 0; if (bottom < upper.y) { if (upper.x > lower.x) bottom_alpha = RectAlpha(pixel_y, pixel_y, bottom, depth); } else { if (bottom < lower.y) pixelWalkMovePointToY(pw, &lower, bottom); bottom_alpha = AlphaAboveLeft(bottom - pixel_y, upper.x - pixel_x, upper.y - pixel_y, lower.x - pixel_x, lower.y - pixel_y, depth); } top_alpha = 0; if (top < upper.y) { if (upper.x > lower.x) top_alpha = RectAlpha(pixel_y, pixel_y, top, depth); } else { if (top < lower.y) pixelWalkMovePointToY(pw, &lower, top); top_alpha = AlphaAboveLeft(top - pixel_y, upper.x - pixel_x, upper.y - pixel_y, lower.x - pixel_x, lower.y - pixel_y, depth); } alpha = bottom_alpha - top_alpha; } return alpha; } #define INCREMENT_X_AND_PIXEL \ { \ pixel_x += xFixed1; \ (*mask.over) (&mask); \ } #define saturateAdd(t, a, b) (((t) = (a) + (b)), \ ((uint8_t) ((t) | (0 - ((t) >> 8))))) #define addAlpha(mask, depth, alpha, temp) (\ (*(mask)->store) ((mask), (alpha == (1 << depth) - 1) ? \ 0xff000000 : \ (saturateAdd (temp, \ alpha << (8 - depth), \ (*(mask)->fetch) (mask) >> 24) << 24)) \ ) void IcRasterizeTrapezoid (IcImage *pMask, const IcTrapezoid *pTrap, int x_off, int y_off) { IcTrapezoid trap = *pTrap; int alpha, temp; IcCompositeOperand mask; int depth = pMask->pixels->depth; int max_alpha = (1 << depth) - 1; int buf_width = pMask->pixels->width; xFixed x_off_fixed = IntToxFixed(x_off); xFixed y_off_fixed = IntToxFixed(y_off); xFixed buf_width_fixed = IntToxFixed(buf_width); PixelWalk left, right; xFixed pixel_x, pixel_y; xFixed first_right_x; xFixed y, y_next; /* trap.left and trap.right must be non-horizontal */ if (trap.left.p1.y == trap.left.p2.y || trap.right.p1.y == trap.right.p2.y) { return; } trap.top += y_off_fixed; trap.bottom += y_off_fixed; trap.left.p1.x += x_off_fixed; trap.left.p1.y += y_off_fixed; trap.left.p2.x += x_off_fixed; trap.left.p2.y += y_off_fixed; trap.right.p1.x += x_off_fixed; trap.right.p1.y += y_off_fixed; trap.right.p2.x += x_off_fixed; trap.right.p2.y += y_off_fixed; pixelWalkInit(&left, &trap.left, trap.top, trap.bottom); pixelWalkInit(&right, &trap.right, trap.top, trap.bottom); if (!IcBuildCompositeOperand (pMask, &mask, 0, xFixedToInt (trap.top), 0, 0)) return; for (y = trap.top; y < trap.bottom; y = y_next) { pixel_y = xFixedFloor (y); y_next = pixel_y + xFixed1; if (y_next > trap.bottom) y_next = trap.bottom; ASSERT (left.row.top.y == y); ASSERT (right.row.top.y == y); pixel_x = xFixedFloor(left.col.left.x); /* * Walk pixels on this row that are left of the * first possibly lit pixel * * pixelWalkNextPixel will change .row.top.y * when the last pixel covered by the edge * is passed */ first_right_x = right.col.left.x; while (right.row.top.y == pixel_y && first_right_x < pixel_x) { /* these are empty */ pixelWalkNextPixel (&right); /* step over */ first_right_x += xFixed1; } (*mask.set) (&mask, xFixedToInt (pixel_x), xFixedToInt (y)); /* * Walk pixels on this row intersected by only trap.left * */ while (left.row.top.y == pixel_y && pixel_x < first_right_x) { alpha = (RectAlpha (pixel_y, y, y_next, depth) - PixelAlpha(pixel_x, pixel_y, y, y_next, &left, depth)); if (alpha > 0) { if (0 <= pixel_x && pixel_x < buf_width_fixed) addAlpha (&mask, depth, alpha, temp); } /* * Step right */ pixelWalkNextPixel(&left); INCREMENT_X_AND_PIXEL; } /* * Either pixels are covered by both edges or * there are fully covered pixels on this row */ if (pixel_x == first_right_x) { /* * Now walk the pixels on this row intersected * by both edges */ while (left.row.top.y == pixel_y && right.row.top.y == pixel_y) { alpha = (PixelAlpha(pixel_x, pixel_y, y, y_next, &right, depth) - PixelAlpha(pixel_x, pixel_y, y, y_next, &left, depth)); if (alpha > 0) { ASSERT (0 <= alpha && alpha <= max_alpha); if (0 <= pixel_x && pixel_x < buf_width_fixed) addAlpha (&mask, depth, alpha, temp); } pixelWalkNextPixel(&left); pixelWalkNextPixel(&right); INCREMENT_X_AND_PIXEL; } } else { /* * Fully covered pixels simply saturate */ alpha = RectAlpha (pixel_y, y, y_next, depth); if (alpha == max_alpha) { while (pixel_x < first_right_x) { if (0 <= pixel_x && pixel_x < buf_width_fixed) (*mask.store) (&mask, 0xff000000); INCREMENT_X_AND_PIXEL; } } else { while (pixel_x < first_right_x) { ASSERT (0 <= alpha && alpha <= max_alpha); if (0 <= pixel_x && pixel_x < buf_width_fixed) addAlpha (&mask, depth, alpha, temp); INCREMENT_X_AND_PIXEL; } } } /* * Finally, pixels intersected only by trap.right */ while (right.row.top.y == pixel_y) { alpha = PixelAlpha(pixel_x, pixel_y, y, y_next, &right, depth); if (alpha > 0) { if (0 <= pixel_x && pixel_x < buf_width_fixed) addAlpha (&mask, depth, alpha, temp); } pixelWalkNextPixel(&right); INCREMENT_X_AND_PIXEL; } /* * If the right edge is now left of the left edge, * the left edge will end up only partially walked, * walk it the rest of the way */ while (left.row.top.y == pixel_y) pixelWalkNextPixel(&left); } } /* Some notes on walking while keeping track of errors in both dimensions: That's really pretty easy. Your bresenham should be walking sub-pixel coordinates rather than pixel coordinates. Now you can calculate the sub-pixel Y coordinate for any arbitrary sub-pixel X coordinate (or vice versa). ey: y error term (distance from current Y sub-pixel to line) * dx ex: x error term (distance from current X sub-pixel to line) * dy dx: difference of X coordinates for line endpoints dy: difference of Y coordinates for line endpoints x: current fixed-point X coordinate y: current fixed-point Y coordinate One of ey or ex will always be zero, depending on whether the distance to the line was measured horizontally or vertically. In moving from x, y to x1, y1: (x1 + e1x/dy) - (x + ex/dy) dx --------------------------- = -- (y1 + e1y/dx) - (y + ey/dx) dy (x1dy + e1x) - (xdy + ex) = (y1dx + e1y) - (ydx + ey) dy(x1 - x) + (e1x - ex) = dx(y1-y) + (e1y - ey) So, if you know y1 and want to know x1: Set e1y to zero and compute the error from x: oex = dx(y1 - y) - ey + ex Compute the number of whole pixels to get close to the line: wx = oex / dy Set x1: Now compute the e1x: e1x = oex - wx * dy A similar operation moves to a known y1. Note that this computation (in general) requires 64 bit arithmetic. I suggest just using the available 64 bit datatype for now, we can optimize the common cases with a few conditionals. */ /* Here's a large-step Bresenham for jogging my memory. void large_bresenham_x_major(x1, y1, x2, y2, x_inc) { int x, y, dx, dy, m; int em_dx, ey_dx; dx = x2 - x1; dy = y2 - y1; m = (x_inc * dy) / dx; em_dx = (x_inc * dy) - m * dx; x = x1; y = y1; ey = 0; set(x,y); while (x < x2) { x += x_inc; y += m; ey_dx += em_dx; if (ey_dx > dx_2) { y++; ey_dx -= dx; } set(x,y); } } */ /* Here are the latest, simplified equations for computing trapezoid coverage of a pixel: alpha_from_area(A) = round(2**depth-1 * A) alpha(o) = 2**depth-1 alpha(a) = alpha_from_area(area(a)) alpha(ab) = alpha_from_area(area(ab)) alpha(b) = alpha(ab) - alpha (a) alpha(abc) = alpha_from_area(area(abc)) alpha(c) = alpha(abc) - alpha(ab) alpha(ad) = alpha_from_area(area(ad)) alpha (d) = alpha(ad) - alpha (a) alpha (abde) = alpha_from_area(area(abde)) alpha (de) = alpha (abde) - alpha (ab) alpha (e) = alpha (de) - alpha (d) alpha (abcdef) = alpha_from_area(area(abcdef)) alpha (def) = alpha (abcdef) - alpha (abc) alpha (f) = alpha (def) - alpha (de) alpha (adg) = alpha_from_area(area(adg)) alpha (g) = alpha (adg) - alpha (ad) alpha (abdegh) = alpha_from_area(area(abdegh)) alpha (gh) = alpha (abdegh) - alpha (abde) alpha (h) = alpha (gh) - alpha (g) alpha (abcdefghi) = alpha_from_area(area(abcdefghi)) = alpha_from_area(area(o)) = alpha_from_area(1) = alpha(o) alpha (ghi) = alpha (abcdefghi) - alpha (abcdef) alpha (i) = alpha (ghi) - alpha (gh) */ /* Latest thoughts from Keith on implementing area/alpha computations: *** 1.16 * 1.16 -> 1.31 *** #define AREA_MULT(w,h) ((w)&(h) == 0x10000 ? 0x80000000 : (((w)*(h) + 1) >> 1) *** (1.16 + 1.16) / 2 -> 1.16 *** #define WIDTH_AVG(x1,x2) (((x1) + (x2) + 1) >> 1) xFixed_1_31 SubpixelArea (xFixed_1_16 x1, xFixed_1_16 x2, xFixed_1_16 y1, xFixed_1_16 y2, xFixed_1_16 bottom) { xFixed_1_16 x_trap; xFixed_1_16 h_top, h_trap, h_bot; xFixed_1_31 area; x_trap = WIDTH_AVG(x1,x2); h_top = y1; h_trap = (y2 - y1); h_bot = (bottom - y2); area = AREA_MULT(x1, h_top) + AREA_MULT(x_trap, h_trap) + AREA_MULT(x2, h_bot); return area; } To convert this xFixed_1_31 value to alpha using 32 bit arithmetic: int AreaAlpha (xFixed_1_31 area, int depth) { return ((area >> bits) * ((1 << depth) - 1)) >> (31 - depth); } Avoiding the branch bubble in the AREA_MULT could be done with either: area = (w * h + 1) >> 1; area |= ((area - 1) & 0x80000000); or #define AREA_MULT(w,h) ((((w)*(h) + 1) >> 1) | ((w)&(h)&0x10000) << 15) depending on your preference, the first takes one less operation but can't be expressed as a macro; the second takes a large constant which may require an additional instruction on some processors. The differences will be swamped by the cost of the multiply. */