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5830a641cc
Pillow/src/libImaging/Draw.c
Stanislau Tsitsianok 5830a641cc
Added more tests
2020-06-29 23:31:04 +03:00

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/*
* The Python Imaging Library.
* $Id$
*
* a simple drawing package for the Imaging library
*
* history:
* 1996-04-13 fl Created.
* 1996-04-30 fl Added transforms and polygon support.
* 1996-08-12 fl Added filled polygons.
* 1996-11-05 fl Fixed float/int confusion in polygon filler
* 1997-07-04 fl Support 32-bit images (C++ would have been nice)
* 1998-09-09 fl Eliminated qsort casts; improved rectangle clipping
* 1998-09-10 fl Fixed fill rectangle to include lower edge (!)
* 1998-12-29 fl Added arc, chord, and pieslice primitives
* 1999-01-10 fl Added some level 2 ("arrow") stuff (experimental)
* 1999-02-06 fl Added bitmap primitive
* 1999-07-26 fl Eliminated a compiler warning
* 1999-07-31 fl Pass ink as void* instead of int
* 2002-12-10 fl Added experimental RGBA-on-RGB drawing
* 2004-09-04 fl Support simple wide lines (no joins)
* 2005-05-25 fl Fixed line width calculation
*
* Copyright (c) 1996-2006 by Fredrik Lundh
* Copyright (c) 1997-2006 by Secret Labs AB.
*
* See the README file for information on usage and redistribution.
*/
/* FIXME: support fill/outline attribute for all filled shapes */
/* FIXME: support zero-winding fill */
/* FIXME: add drawing context, support affine transforms */
/* FIXME: support clip window (and mask?) */
#include "Imaging.h"
#include <math.h>
#include <stdint.h>
#define CEIL(v) (int) ceil(v)
#define FLOOR(v) ((v) >= 0.0 ? (int) (v) : (int) floor(v))
#define INK8(ink) (*(UINT8*)ink)
/*
* Rounds around zero (up=away from zero, down=towards zero)
* This guarantees that ROUND_UP|DOWN(f) == -ROUND_UP|DOWN(-f)
*/
#define ROUND_UP(f) ((int) ((f) >= 0.0 ? floor((f) + 0.5F) : -floor(fabs(f) + 0.5F)))
#define ROUND_DOWN(f) ((int) ((f) >= 0.0 ? ceil((f) - 0.5F) : -ceil(fabs(f) - 0.5F)))
/* -------------------------------------------------------------------- */
/* Primitives */
/* -------------------------------------------------------------------- */
typedef struct {
/* edge descriptor for polygon engine */
int d;
int x0, y0;
int xmin, ymin, xmax, ymax;
float dx;
} Edge;
/* Type used in "polygon*" functions */
typedef void (*hline_handler)(Imaging, int, int, int, int);
static inline void
point8(Imaging im, int x, int y, int ink)
{
if (x >= 0 && x < im->xsize && y >= 0 && y < im->ysize) {
if (strncmp(im->mode, "I;16", 4) == 0) {
im->image8[y][x*2] = (UINT8) ink;
im->image8[y][x*2+1] = (UINT8) ink;
} else {
im->image8[y][x] = (UINT8) ink;
}
}
}
static inline void
point32(Imaging im, int x, int y, int ink)
{
if (x >= 0 && x < im->xsize && y >= 0 && y < im->ysize) {
im->image32[y][x] = ink;
}
}
static inline void
point32rgba(Imaging im, int x, int y, int ink)
{
unsigned int tmp1;
if (x >= 0 && x < im->xsize && y >= 0 && y < im->ysize) {
UINT8* out = (UINT8*) im->image[y]+x*4;
UINT8* in = (UINT8*) &ink;
out[0] = BLEND(in[3], out[0], in[0], tmp1);
out[1] = BLEND(in[3], out[1], in[1], tmp1);
out[2] = BLEND(in[3], out[2], in[2], tmp1);
}
}
static inline void
hline8(Imaging im, int x0, int y0, int x1, int ink)
{
int tmp, pixelwidth;
if (y0 >= 0 && y0 < im->ysize) {
if (x0 > x1) {
tmp = x0, x0 = x1, x1 = tmp;
}
if (x0 < 0) {
x0 = 0;
} else if (x0 >= im->xsize) {
return;
}
if (x1 < 0) {
return;
} else if (x1 >= im->xsize) {
x1 = im->xsize-1;
}
if (x0 <= x1) {
pixelwidth = strncmp(im->mode, "I;16", 4) == 0 ? 2 : 1;
memset(im->image8[y0] + x0 * pixelwidth, (UINT8) ink,
(x1 - x0 + 1) * pixelwidth);
}
}
}
static inline void
hline32(Imaging im, int x0, int y0, int x1, int ink)
{
int tmp;
INT32* p;
if (y0 >= 0 && y0 < im->ysize) {
if (x0 > x1) {
tmp = x0, x0 = x1, x1 = tmp;
}
if (x0 < 0) {
x0 = 0;
} else if (x0 >= im->xsize) {
return;
}
if (x1 < 0) {
return;
} else if (x1 >= im->xsize) {
x1 = im->xsize-1;
}
p = im->image32[y0];
while (x0 <= x1) {
p[x0++] = ink;
}
}
}
static inline void
hline32rgba(Imaging im, int x0, int y0, int x1, int ink)
{
int tmp;
unsigned int tmp1;
if (y0 >= 0 && y0 < im->ysize) {
if (x0 > x1) {
tmp = x0, x0 = x1, x1 = tmp;
}
if (x0 < 0) {
x0 = 0;
} else if (x0 >= im->xsize) {
return;
}
if (x1 < 0) {
return;
} else if (x1 >= im->xsize) {
x1 = im->xsize-1;
}
if (x0 <= x1) {
UINT8* out = (UINT8*) im->image[y0]+x0*4;
UINT8* in = (UINT8*) &ink;
while (x0 <= x1) {
out[0] = BLEND(in[3], out[0], in[0], tmp1);
out[1] = BLEND(in[3], out[1], in[1], tmp1);
out[2] = BLEND(in[3], out[2], in[2], tmp1);
x0++; out += 4;
}
}
}
}
static inline void
line8(Imaging im, int x0, int y0, int x1, int y1, int ink)
{
int i, n, e;
int dx, dy;
int xs, ys;
/* normalize coordinates */
dx = x1-x0;
if (dx < 0) {
dx = -dx, xs = -1;
} else {
xs = 1;
}
dy = y1-y0;
if (dy < 0) {
dy = -dy, ys = -1;
} else {
ys = 1;
}
n = (dx > dy) ? dx : dy;
if (dx == 0) {
/* vertical */
for (i = 0; i < dy; i++) {
point8(im, x0, y0, ink);
y0 += ys;
}
} else if (dy == 0) {
/* horizontal */
for (i = 0; i < dx; i++) {
point8(im, x0, y0, ink);
x0 += xs;
}
} else if (dx > dy) {
/* bresenham, horizontal slope */
n = dx;
dy += dy;
e = dy - dx;
dx += dx;
for (i = 0; i < n; i++) {
point8(im, x0, y0, ink);
if (e >= 0) {
y0 += ys;
e -= dx;
}
e += dy;
x0 += xs;
}
} else {
/* bresenham, vertical slope */
n = dy;
dx += dx;
e = dx - dy;
dy += dy;
for (i = 0; i < n; i++) {
point8(im, x0, y0, ink);
if (e >= 0) {
x0 += xs;
e -= dy;
}
e += dx;
y0 += ys;
}
}
}
static inline void
line32(Imaging im, int x0, int y0, int x1, int y1, int ink)
{
int i, n, e;
int dx, dy;
int xs, ys;
/* normalize coordinates */
dx = x1-x0;
if (dx < 0) {
dx = -dx, xs = -1;
} else {
xs = 1;
}
dy = y1-y0;
if (dy < 0) {
dy = -dy, ys = -1;
} else {
ys = 1;
}
n = (dx > dy) ? dx : dy;
if (dx == 0) {
/* vertical */
for (i = 0; i < dy; i++) {
point32(im, x0, y0, ink);
y0 += ys;
}
} else if (dy == 0) {
/* horizontal */
for (i = 0; i < dx; i++) {
point32(im, x0, y0, ink);
x0 += xs;
}
} else if (dx > dy) {
/* bresenham, horizontal slope */
n = dx;
dy += dy;
e = dy - dx;
dx += dx;
for (i = 0; i < n; i++) {
point32(im, x0, y0, ink);
if (e >= 0) {
y0 += ys;
e -= dx;
}
e += dy;
x0 += xs;
}
} else {
/* bresenham, vertical slope */
n = dy;
dx += dx;
e = dx - dy;
dy += dy;
for (i = 0; i < n; i++) {
point32(im, x0, y0, ink);
if (e >= 0) {
x0 += xs;
e -= dy;
}
e += dx;
y0 += ys;
}
}
}
static inline void
line32rgba(Imaging im, int x0, int y0, int x1, int y1, int ink)
{
int i, n, e;
int dx, dy;
int xs, ys;
/* normalize coordinates */
dx = x1-x0;
if (dx < 0) {
dx = -dx, xs = -1;
} else {
xs = 1;
}
dy = y1-y0;
if (dy < 0) {
dy = -dy, ys = -1;
} else {
ys = 1;
}
n = (dx > dy) ? dx : dy;
if (dx == 0) {
/* vertical */
for (i = 0; i < dy; i++) {
point32rgba(im, x0, y0, ink);
y0 += ys;
}
} else if (dy == 0) {
/* horizontal */
for (i = 0; i < dx; i++) {
point32rgba(im, x0, y0, ink);
x0 += xs;
}
} else if (dx > dy) {
/* bresenham, horizontal slope */
n = dx;
dy += dy;
e = dy - dx;
dx += dx;
for (i = 0; i < n; i++) {
point32rgba(im, x0, y0, ink);
if (e >= 0) {
y0 += ys;
e -= dx;
}
e += dy;
x0 += xs;
}
} else {
/* bresenham, vertical slope */
n = dy;
dx += dx;
e = dx - dy;
dy += dy;
for (i = 0; i < n; i++) {
point32rgba(im, x0, y0, ink);
if (e >= 0) {
x0 += xs;
e -= dy;
}
e += dx;
y0 += ys;
}
}
}
static int
x_cmp(const void *x0, const void *x1)
{
float diff = *((float*)x0) - *((float*)x1);
if (diff < 0) {
return -1;
} else if (diff > 0) {
return 1;
} else {
return 0;
}
}
static void
draw_horizontal_lines(Imaging im, int n, Edge *e, int ink, int *x_pos, int y, hline_handler hline)
{
int i;
for (i = 0; i < n; i++) {
if (e[i].ymin == y && e[i].ymin == e[i].ymax) {
int xmax;
int xmin = e[i].xmin;
if (*x_pos < xmin) {
// Line would be after the current position
continue;
}
xmax = e[i].xmax;
if (*x_pos > xmin) {
// Line would be partway through x_pos, so increase the starting point
xmin = *x_pos;
if (xmax < xmin) {
// Line would now end before it started
continue;
}
}
(*hline)(im, xmin, e[i].ymin, xmax, ink);
*x_pos = xmax+1;
}
}
}
/*
* Filled polygon draw function using scan line algorithm.
*/
static inline int
polygon_generic(Imaging im, int n, Edge *e, int ink, int eofill,
hline_handler hline)
{
Edge** edge_table;
float* xx;
int edge_count = 0;
int ymin = im->ysize - 1;
int ymax = 0;
int i;
if (n <= 0) {
return 0;
}
/* Initialize the edge table and find polygon boundaries */
/* malloc check ok, using calloc */
edge_table = calloc(n, sizeof(Edge*));
if (!edge_table) {
return -1;
}
for (i = 0; i < n; i++) {
if (ymin > e[i].ymin) {
ymin = e[i].ymin;
}
if (ymax < e[i].ymax) {
ymax = e[i].ymax;
}
if (e[i].ymin == e[i].ymax) {
continue;
}
edge_table[edge_count++] = (e + i);
}
if (ymin < 0) {
ymin = 0;
}
if (ymax > im->ysize) {
ymax = im->ysize;
}
/* Process the edge table with a scan line searching for intersections */
/* malloc check ok, using calloc */
xx = calloc(edge_count * 2, sizeof(float));
if (!xx) {
free(edge_table);
return -1;
}
for (; ymin <= ymax; ymin++) {
int j = 0;
int x_pos = 0;
for (i = 0; i < edge_count; i++) {
Edge* current = edge_table[i];
if (ymin >= current->ymin && ymin <= current->ymax) {
xx[j++] = (ymin - current->y0) * current->dx + current->x0;
}
/* Needed to draw consistent polygons */
if (ymin == current->ymax && ymin < ymax) {
xx[j] = xx[j - 1];
j++;
}
}
qsort(xx, j, sizeof(float), x_cmp);
for (i = 1; i < j; i += 2) {
int x_end = ROUND_DOWN(xx[i]);
if (x_end < x_pos) {
// Line would be before the current position
continue;
}
draw_horizontal_lines(im, n, e, ink, &x_pos, ymin, hline);
if (x_end < x_pos) {
// Line would be before the current position
continue;
}
int x_start = ROUND_UP(xx[i-1]);
if (x_pos > x_start) {
// Line would be partway through x_pos, so increase the starting point
x_start = x_pos;
if (x_end < x_start) {
// Line would now end before it started
continue;
}
}
(*hline)(im, x_start, ymin, x_end, ink);
x_pos = x_end+1;
}
draw_horizontal_lines(im, n, e, ink, &x_pos, ymin, hline);
}
free(xx);
free(edge_table);
return 0;
}
static inline int
polygon8(Imaging im, int n, Edge *e, int ink, int eofill)
{
return polygon_generic(im, n, e, ink, eofill, hline8);
}
static inline int
polygon32(Imaging im, int n, Edge *e, int ink, int eofill)
{
return polygon_generic(im, n, e, ink, eofill, hline32);
}
static inline int
polygon32rgba(Imaging im, int n, Edge *e, int ink, int eofill)
{
return polygon_generic(im, n, e, ink, eofill, hline32rgba);
}
static inline void
add_edge(Edge *e, int x0, int y0, int x1, int y1)
{
/* printf("edge %d %d %d %d\n", x0, y0, x1, y1); */
if (x0 <= x1) {
e->xmin = x0, e->xmax = x1;
} else {
e->xmin = x1, e->xmax = x0;
}
if (y0 <= y1) {
e->ymin = y0, e->ymax = y1;
} else {
e->ymin = y1, e->ymax = y0;
}
if (y0 == y1) {
e->d = 0;
e->dx = 0.0;
} else {
e->dx = ((float)(x1-x0)) / (y1-y0);
if (y0 == e->ymin) {
e->d = 1;
} else {
e->d = -1;
}
}
e->x0 = x0;
e->y0 = y0;
}
typedef struct {
void (*point)(Imaging im, int x, int y, int ink);
void (*hline)(Imaging im, int x0, int y0, int x1, int ink);
void (*line)(Imaging im, int x0, int y0, int x1, int y1, int ink);
int (*polygon)(Imaging im, int n, Edge *e, int ink, int eofill);
} DRAW;
DRAW draw8 = { point8, hline8, line8, polygon8 };
DRAW draw32 = { point32, hline32, line32, polygon32 };
DRAW draw32rgba = { point32rgba, hline32rgba, line32rgba, polygon32rgba };
/* -------------------------------------------------------------------- */
/* Interface */
/* -------------------------------------------------------------------- */
#define DRAWINIT()\
if (im->image8) {\
draw = &draw8;\
ink = INK8(ink_);\
} else {\
draw = (op) ? &draw32rgba : &draw32; \
memcpy(&ink, ink_, sizeof(ink)); \
}
int
ImagingDrawPoint(Imaging im, int x0, int y0, const void* ink_, int op)
{
DRAW* draw;
INT32 ink;
DRAWINIT();
draw->point(im, x0, y0, ink);
return 0;
}
int
ImagingDrawLine(Imaging im, int x0, int y0, int x1, int y1, const void* ink_,
int op)
{
DRAW* draw;
INT32 ink;
DRAWINIT();
draw->line(im, x0, y0, x1, y1, ink);
return 0;
}
int
ImagingDrawWideLine(Imaging im, int x0, int y0, int x1, int y1,
const void* ink_, int width, int op)
{
DRAW* draw;
INT32 ink;
int dx, dy;
double big_hypotenuse, small_hypotenuse, ratio_max, ratio_min;
int dxmin, dxmax, dymin, dymax;
Edge e[4];
DRAWINIT();
dx = x1-x0;
dy = y1-y0;
if (dx == 0 && dy == 0) {
draw->point(im, x0, y0, ink);
return 0;
}
big_hypotenuse = sqrt((double) (dx*dx + dy*dy));
small_hypotenuse = (width - 1) / 2.0;
ratio_max = ROUND_UP(small_hypotenuse) / big_hypotenuse;
ratio_min = ROUND_DOWN(small_hypotenuse) / big_hypotenuse;
dxmin = ROUND_DOWN(ratio_min * dy);
dxmax = ROUND_DOWN(ratio_max * dy);
dymin = ROUND_DOWN(ratio_min * dx);
dymax = ROUND_DOWN(ratio_max * dx);
{
int vertices[4][2] = {
{x0 - dxmin, y0 + dymax},
{x1 - dxmin, y1 + dymax},
{x1 + dxmax, y1 - dymin},
{x0 + dxmax, y0 - dymin}
};
add_edge(e+0, vertices[0][0], vertices[0][1], vertices[1][0], vertices[1][1]);
add_edge(e+1, vertices[1][0], vertices[1][1], vertices[2][0], vertices[2][1]);
add_edge(e+2, vertices[2][0], vertices[2][1], vertices[3][0], vertices[3][1]);
add_edge(e+3, vertices[3][0], vertices[3][1], vertices[0][0], vertices[0][1]);
draw->polygon(im, 4, e, ink, 0);
}
return 0;
}
int
ImagingDrawRectangle(Imaging im, int x0, int y0, int x1, int y1,
const void* ink_, int fill, int width, int op)
{
int i;
int y;
int tmp;
DRAW* draw;
INT32 ink;
DRAWINIT();
if (y0 > y1) {
tmp = y0, y0 = y1, y1 = tmp;
}
if (fill) {
if (y0 < 0) {
y0 = 0;
} else if (y0 >= im->ysize) {
return 0;
}
if (y1 < 0) {
return 0;
} else if (y1 > im->ysize) {
y1 = im->ysize;
}
for (y = y0; y <= y1; y++) {
draw->hline(im, x0, y, x1, ink);
}
} else {
/* outline */
if (width == 0) {
width = 1;
}
for (i = 0; i < width; i++) {
draw->hline(im, x0, y0+i, x1, ink);
draw->hline(im, x0, y1-i, x1, ink);
draw->line(im, x1-i, y0, x1-i, y1, ink);
draw->line(im, x0+i, y1, x0+i, y0, ink);
}
}
return 0;
}
int
ImagingDrawPolygon(Imaging im, int count, int* xy, const void* ink_,
int fill, int op)
{
int i, n;
DRAW* draw;
INT32 ink;
if (count <= 0) {
return 0;
}
DRAWINIT();
if (fill) {
/* Build edge list */
/* malloc check ok, using calloc */
Edge* e = calloc(count, sizeof(Edge));
if (!e) {
(void) ImagingError_MemoryError();
return -1;
}
for (i = n = 0; i < count-1; i++) {
add_edge(&e[n++], xy[i+i], xy[i+i+1], xy[i+i+2], xy[i+i+3]);
}
if (xy[i+i] != xy[0] || xy[i+i+1] != xy[1]) {
add_edge(&e[n++], xy[i+i], xy[i+i+1], xy[0], xy[1]);
}
draw->polygon(im, n, e, ink, 0);
free(e);
} else {
/* Outline */
for (i = 0; i < count-1; i++) {
draw->line(im, xy[i+i], xy[i+i+1], xy[i+i+2], xy[i+i+3], ink);
}
draw->line(im, xy[i+i], xy[i+i+1], xy[0], xy[1], ink);
}
return 0;
}
int
ImagingDrawBitmap(Imaging im, int x0, int y0, Imaging bitmap, const void* ink,
int op)
{
return ImagingFill2(
im, ink, bitmap,
x0, y0, x0 + bitmap->xsize, y0 + bitmap->ysize
);
}
/* -------------------------------------------------------------------- */
/* standard shapes */
// Imagine 2D plane and ellipse with center in (0, 0) and semi-major axes a and b.
// Then quarter_* stuff approximates its top right quarter (x, y >= 0) with integer
// points from set {(2x+x0, 2y+y0) | x,y in Z} where x0, y0 are from {0, 1} and
// are such that point (a, b) is in the set.
typedef struct {
int32_t a, b, cx, cy, ex, ey;
int64_t a2, b2, a2b2;
int8_t finished;
} quarter_state;
void quarter_init(quarter_state* s, int32_t a, int32_t b) {
if (a < 0 || b < 0) {
s->finished = 1;
} else {
s->a = a;
s->b = b;
s->cx = a;
s->cy = b % 2;
s->ex = a % 2;
s->ey = b;
s->a2 = a * a;
s->b2 = b * b;
s->a2b2 = s->a2 * s->b2;
s->finished = 0;
}
}
// deviation of the point from ellipse curve, basically a substitution
// of the point into the ellipse equation
int64_t quarter_delta(quarter_state* s, int64_t x, int64_t y) {
return llabs(s->a2 * y * y + s->b2 * x * x - s->a2b2);
}
int8_t quarter_next(quarter_state* s, int32_t* ret_x, int32_t* ret_y) {
if (s->finished) {
return -1;
}
*ret_x = s->cx;
*ret_y = s->cy;
if (s->cx == s->ex && s->cy == s->ey) {
s->finished = 1;
} else {
// bresenham's algorithm, possible optimization: only consider 2 of 3
// next points depending on current slope
int32_t nx = s->cx;
int32_t ny = s->cy + 2;
int64_t ndelta = quarter_delta(s, nx, ny);
if (nx > 1) {
int64_t newdelta = quarter_delta(s, s->cx - 2, s->cy + 2);
if (ndelta > newdelta) {
nx = s->cx - 2;
ny = s->cy + 2;
ndelta = newdelta;
}
newdelta = quarter_delta(s, s->cx - 2, s->cy);
if (ndelta > newdelta) {
nx = s->cx - 2;
ny = s->cy;
}
}
s->cx = nx;
s->cy = ny;
}
return 0;
}
// quarter_* stuff can "draw" a quarter of an ellipse with thickness 1, great.
// Now we use ellipse_* stuff to join all four quarters of two different sized
// ellipses and receive horizontal segments of a complete ellipse with
// specified thickness.
//
// Still using integer grid with step 2 at this point (like in quarter_*)
// to ease angle clipping in future.
typedef struct {
quarter_state st_o, st_i;
int32_t py, pl, pr;
int32_t cy[4], cl[4], cr[4];
int8_t bufcnt;
int8_t finished;
int8_t leftmost;
} ellipse_state;
void ellipse_init(ellipse_state* s, int32_t a, int32_t b, int32_t w) {
s->bufcnt = 0;
s->leftmost = a % 2;
quarter_init(&s->st_o, a, b);
if (w < 1 || quarter_next(&s->st_o, &s->pr, &s->py) == -1) {
s->finished = 1;
} else {
s->finished = 0;
quarter_init(&s->st_i, a - 2 * (w - 1), b - 2 * (w - 1));
s->pl = s->leftmost;
}
}
int8_t ellipse_next(ellipse_state* s, int32_t* ret_x0, int32_t* ret_y, int32_t* ret_x1) {
if (s->bufcnt == 0) {
if (s->finished) {
return -1;
}
int32_t y = s->py;
int32_t l = s->pl;
int32_t r = s->pr;
int32_t cx = 0, cy = 0;
int8_t next_ret;
while ((next_ret = quarter_next(&s->st_o, &cx, &cy)) != -1 && cy <= y) {
}
if (next_ret == -1) {
s->finished = 1;
} else {
s->pr = cx;
s->py = cy;
}
while ((next_ret = quarter_next(&s->st_i, &cx, &cy)) != -1 && cy <= y) {
l = cx;
}
s->pl = next_ret == -1 ? s->leftmost : cx;
if ((l > 0 || l < r) && y > 0) {
s->cl[s->bufcnt] = l == 0 ? 2 : l;
s->cy[s->bufcnt] = y;
s->cr[s->bufcnt] = r;
++s->bufcnt;
}
if (y > 0) {
s->cl[s->bufcnt] = -r;
s->cy[s->bufcnt] = y;
s->cr[s->bufcnt] = -l;
++s->bufcnt;
}
if (l > 0 || l < r) {
s->cl[s->bufcnt] = l == 0 ? 2 : l;
s->cy[s->bufcnt] = -y;
s->cr[s->bufcnt] = r;
++s->bufcnt;
}
s->cl[s->bufcnt] = -r;
s->cy[s->bufcnt] = -y;
s->cr[s->bufcnt] = -l;
++s->bufcnt;
}
--s->bufcnt;
*ret_x0 = s->cl[s->bufcnt];
*ret_y = s->cy[s->bufcnt];
*ret_x1 = s->cr[s->bufcnt];
return 0;
}
// Clipping tree consists of half-plane clipping nodes and combining nodes.
// We can throw a horizontal segment in such a tree and collect an ordered set
// of resulting disjoint clipped segments organized into a sorted linked list
// of their end points.
typedef enum {
CT_AND, // intersection
CT_OR, // union
CT_CLIP // half-plane clipping
} clip_type;
typedef struct clip_node {
clip_type type;
double a, b, c; // half-plane coeffs, only used in clipping nodes
struct clip_node* l; // child pointers, are only non-NULL in combining nodes
struct clip_node* r;
} clip_node;
// Linked list for the ends of the clipped horizontal segments.
// Since the segment is always horizontal, we don't need to store Y coordinate.
typedef struct event_list {
int32_t x;
int8_t type; // used internally, 1 for the left end (smaller X), -1 for the
// right end; pointless in output since the output segments
// are disjoint, therefore the types would always come in pairs
// and interchange (1 -1 1 -1 ...)
struct event_list* next;
} event_list;
// Mirrors all the clipping nodes of the tree relative to the y = x line.
void clip_tree_transpose(clip_node* root) {
if (root != NULL) {
if (root->type == CT_CLIP) {
double t = root->a;
root->a = root->b;
root->b = t;
}
clip_tree_transpose(root->l);
clip_tree_transpose(root->r);
}
}
// Outputs a sequence of open-close events (types -1 and 1) for
// non-intersecting segments sorted by X coordinate.
// Combining nodes (AND, OR) may also accept sequences for intersecting
// segments, i.e. something like correct bracket sequences.
int clip_tree_do_clip(clip_node* root, int32_t x0, int32_t y, int32_t x1, event_list** ret) {
if (root == NULL) {
event_list* start = malloc(sizeof(event_list));
if (!start) {
ImagingError_MemoryError();
return -1;
}
event_list* end = malloc(sizeof(event_list));
if (!end) {
free(start);
ImagingError_MemoryError();
return -1;
}
start->x = x0;
start->type = 1;
start->next = end;
end->x = x1;
end->type = -1;
end->next = NULL;
*ret = start;
return 0;
}
if (root->type == CT_CLIP) {
double eps = 1e-9;
double A = root->a;
double B = root->b;
double C = root->c;
if (fabs(A) < eps) {
if (B * y + C < -eps) {
x0 = 1;
x1 = 0;
}
} else {
// X of intersection
double ix = - (B * y + C) / A;
if (A * x0 + B * y + C < eps) {
x0 = round(fmax(x0, ix));
}
if (A * x1 + B * y + C < eps) {
x1 = round(fmin(x1, ix));
}
}
if (x0 <= x1) {
event_list* start = malloc(sizeof(event_list));
if (!start) {
ImagingError_MemoryError();
return -1;
}
event_list* end = malloc(sizeof(event_list));
if (!end) {
free(start);
ImagingError_MemoryError();
return -1;
}
start->x = x0;
start->type = 1;
start->next = end;
end->x = x1;
end->type = -1;
end->next = NULL;
*ret = start;
} else {
*ret = NULL;
}
return 0;
}
if (root->type == CT_OR || root->type == CT_AND) {
event_list* l1;
event_list* l2;
if (clip_tree_do_clip(root->l, x0, y, x1, &l1) < 0) {
return -1;
}
if (clip_tree_do_clip(root->r, x0, y, x1, &l2) < 0) {
while (l1) {
l2 = l1->next;
free(l1);
l1 = l2;
}
return -1;
}
*ret = NULL;
event_list* tail = NULL;
int32_t k1 = 0;
int32_t k2 = 0;
while (l1 != NULL || l2 != NULL) {
event_list* t;
if (l2 == NULL || (l1 != NULL && (l1->x < l2->x || (l1->x == l2->x && l1->type > l2->type)))) {
t = l1;
k1 += t->type;
assert(k1 >= 0);
l1 = l1->next;
} else {
t = l2;
k2 += t->type;
assert(k2 >= 0);
l2 = l2->next;
}
t->next = NULL;
if ((root->type == CT_OR && (
(t->type == 1 && (tail == NULL || tail->type == -1)) ||
(t->type == -1 && k1 == 0 && k2 == 0)
)) ||
(root->type == CT_AND && (
(t->type == 1 && (tail == NULL || tail->type == -1) && k1 > 0 && k2 > 0) ||
(t->type == -1 && tail != NULL && tail->type == 1 && (k1 == 0 || k2 == 0))
))) {
if (tail == NULL) {
*ret = t;
} else {
tail->next = t;
}
tail = t;
} else {
free(t);
}
}
return 0;
}
*ret = NULL;
return 0;
}
// One more layer of processing on top of the regular ellipse.
// Uses the clipping tree.
// Used for producing ellipse derivatives such as arc, chord, pie, etc.
typedef struct {
ellipse_state st;
clip_node* root;
clip_node nodes[7];
int32_t node_count;
event_list* head;
int32_t y;
} clip_ellipse_state;
typedef void (*clip_ellipse_init)(clip_ellipse_state*, int32_t, int32_t, int32_t, float, float);
void debug_clip_tree(clip_node* root, int space) {
if (root == NULL) {
return;
}
if (root->type == CT_CLIP) {
int t = space;
while (t--) {
fputc(' ', stderr);
}
fprintf(stderr, "clip %+fx%+fy%+f > 0\n", root->a, root->b, root->c);
} else {
debug_clip_tree(root->l, space + 2);
int t = space;
while (t--) {
fputc(' ', stderr);
}
fprintf(stderr, "%s\n", root->type == CT_AND ? "and" : "or");
debug_clip_tree(root->r, space + 2);
}
if (space == 0) {
fputc('\n', stderr);
}
}
// Resulting angles will satisfy 0 <= al < 360, al <= ar <= al + 360
void normalize_angles(float* al, float* ar) {
if (*ar - *al >= 360) {
*al = 0;
*ar = 360;
} else {
*al = fmod(*al < 0 ? 360 - (fmod(-*al, 360)) : *al, 360);
*ar = *al + fmod(*ar < *al ? 360 - fmod(*al - *ar, 360) : *ar - *al, 360);
}
}
// An arc with caps orthogonal to the ellipse curve.
void arc_init(clip_ellipse_state* s, int32_t a, int32_t b, int32_t w, float al, float ar) {
if (a < b) {
// transpose the coordinate system
arc_init(s, b, a, w, 90 - ar, 90 - al);
ellipse_init(&s->st, a, b, w);
clip_tree_transpose(s->root);
} else {
// a >= b, based on "wide" ellipse
ellipse_init(&s->st, a, b, w);
s->head = NULL;
s->node_count = 0;
normalize_angles(&al, &ar);
// building clipping tree, a lot of different cases
if (ar == al + 360) {
s->root = NULL;
} else {
clip_node* lc = s->nodes + s->node_count++;
clip_node* rc = s->nodes + s->node_count++;
lc->l = lc->r = rc->l = rc->r = NULL;
lc->type = rc->type = CT_CLIP;
lc->a = -a * sin(al * M_PI / 180.0);
lc->b = b * cos(al * M_PI / 180.0);
lc->c = (a * a - b * b) * sin(al * M_PI / 90.0) / 2.0;
rc->a = a * sin(ar * M_PI / 180.0);
rc->b = -b * cos(ar * M_PI / 180.0);
rc->c = (b * b - a * a) * sin(ar * M_PI / 90.0) / 2.0;
if (fmod(al, 180) == 0 || fmod(ar, 180) == 0) {
s->root = s->nodes + s->node_count++;
s->root->l = lc;
s->root->r = rc;
s->root->type = ar - al < 180 ? CT_AND : CT_OR;
} else if (((int)(al / 180) + (int)(ar / 180)) % 2 == 1) {
s->root = s->nodes + s->node_count++;
s->root->l = s->nodes + s->node_count++;
s->root->l->l = s->nodes + s->node_count++;
s->root->l->r = lc;
s->root->r = s->nodes + s->node_count++;
s->root->r->l = s->nodes + s->node_count++;
s->root->r->r = rc;
s->root->type = CT_OR;
s->root->l->type = CT_AND;
s->root->r->type = CT_AND;
s->root->l->l->type = CT_CLIP;
s->root->r->l->type = CT_CLIP;
s->root->l->l->l = s->root->l->l->r = NULL;
s->root->r->l->l = s->root->r->l->r = NULL;
s->root->l->l->a = s->root->l->l->c = 0;
s->root->r->l->a = s->root->r->l->c = 0;
s->root->l->l->b = (int)(al / 180) % 2 == 0 ? 1 : -1;
s->root->r->l->b = (int)(ar / 180) % 2 == 0 ? 1 : -1;
} else {
s->root = s->nodes + s->node_count++;
s->root->l = s->nodes + s->node_count++;
s->root->r = s->nodes + s->node_count++;
s->root->type = s->root->l->type = ar - al < 180 ? CT_AND : CT_OR;
s->root->l->l = lc;
s->root->l->r = rc;
s->root->r->type = CT_CLIP;
s->root->r->l = s->root->r->r = NULL;
s->root->r->a = s->root->r->c = 0;
s->root->r->b = ar < 180 || ar > 540 ? 1 : -1;
}
}
}
}
// A chord line.
void chord_line_init(clip_ellipse_state* s, int32_t a, int32_t b, int32_t w, float al, float ar) {
ellipse_init(&s->st, a, b, a + b + 1);
s->head = NULL;
s->node_count = 0;
// line equation for chord
double xl = a * cos(al * M_PI / 180.0), xr = a * cos(ar * M_PI / 180.0);
double yl = b * sin(al * M_PI / 180.0), yr = b * sin(ar * M_PI / 180.0);
s->root = s->nodes + s->node_count++;
s->root->l = s->nodes + s->node_count++;
s->root->r = s->nodes + s->node_count++;
s->root->type = CT_AND;
s->root->l->type = s->root->r->type = CT_CLIP;
s->root->l->l = s->root->l->r = s->root->r->l = s->root->r->r = NULL;
s->root->l->a = yr - yl;
s->root->l->b = xl - xr;
s->root->l->c = -(s->root->l->a * xl + s->root->l->b * yl);
s->root->r->a = -s->root->l->a;
s->root->r->b = -s->root->l->b;
s->root->r->c = 2 * w * sqrt(pow(s->root->l->a, 2.0) + pow(s->root->l->b, 2.0)) - s->root->l->c;
}
// Pie side.
void pie_side_init(clip_ellipse_state* s, int32_t a, int32_t b, int32_t w, float al, float _) {
ellipse_init(&s->st, a, b, a + b + 1);
s->head = NULL;
s->node_count = 0;
double xl = a * cos(al * M_PI / 180.0);
double yl = b * sin(al * M_PI / 180.0);
double a1 = -yl;
double b1 = xl;
double c1 = w * sqrt(a1 * a1 + b1 * b1);
s->root = s->nodes + s->node_count++;
s->root->type = CT_AND;
s->root->l = s->nodes + s->node_count++;
s->root->l->type = CT_AND;
clip_node* cnode;
cnode = s->nodes + s->node_count++;
cnode->l = cnode->r = NULL;
cnode->type = CT_CLIP;
cnode->a = a1;
cnode->b = b1;
cnode->c = c1;
s->root->l->l = cnode;
cnode = s->nodes + s->node_count++;
cnode->l = cnode->r = NULL;
cnode->type = CT_CLIP;
cnode->a = -a1;
cnode->b = -b1;
cnode->c = c1;
s->root->l->r = cnode;
cnode = s->nodes + s->node_count++;
cnode->l = cnode->r = NULL;
cnode->type = CT_CLIP;
cnode->a = b1;
cnode->b = -a1;
cnode->c = 0;
s->root->r = cnode;
}
// A chord.
void chord_init(clip_ellipse_state* s, int32_t a, int32_t b, int32_t w, float al, float ar) {
ellipse_init(&s->st, a, b, w);
s->head = NULL;
s->node_count = 0;
// line equation for chord
double xl = a * cos(al * M_PI / 180.0), xr = a * cos(ar * M_PI / 180.0);
double yl = b * sin(al * M_PI / 180.0), yr = b * sin(ar * M_PI / 180.0);
s->root = s->nodes + s->node_count++;
s->root->l = s->root->r = NULL;
s->root->type = CT_CLIP;
s->root->a = yr - yl;
s->root->b = xl - xr;
s->root->c = -(s->root->a * xl + s->root->b * yl);
}
// A pie. Can also be used to draw an arc with ugly sharp caps.
void pie_init(clip_ellipse_state* s, int32_t a, int32_t b, int32_t w, float al, float ar) {
ellipse_init(&s->st, a, b, w);
s->head = NULL;
s->node_count = 0;
// line equations for pie sides
double xl = a * cos(al * M_PI / 180.0), xr = a * cos(ar * M_PI / 180.0);
double yl = b * sin(al * M_PI / 180.0), yr = b * sin(ar * M_PI / 180.0);
clip_node* lc = s->nodes + s->node_count++;
clip_node* rc = s->nodes + s->node_count++;
lc->l = lc->r = rc->l = rc->r = NULL;
lc->type = rc->type = CT_CLIP;
lc->a = -yl;
lc->b = xl;
lc->c = 0;
rc->a = yr;
rc->b = -xr;
rc->c = 0;
s->root = s->nodes + s->node_count++;
s->root->l = lc;
s->root->r = rc;
s->root->type = ar - al < 180 ? CT_AND : CT_OR;
}
void clip_ellipse_free(clip_ellipse_state* s) {
while (s->head != NULL) {
event_list* t = s->head;
s->head = s->head->next;
free(t);
}
}
int8_t clip_ellipse_next(clip_ellipse_state* s, int32_t* ret_x0, int32_t* ret_y, int32_t* ret_x1) {
int32_t x0, y, x1;
while (s->head == NULL && ellipse_next(&s->st, &x0, &y, &x1) >= 0) {
if (clip_tree_do_clip(s->root, x0, y, x1, &s->head) < 0) {
return -2;
}
s->y = y;
}
if (s->head != NULL) {
*ret_y = s->y;
event_list* t = s->head;
s->head = s->head->next;
*ret_x0 = t->x;
free(t);
t = s->head;
assert(t != NULL);
s->head = s->head->next;
*ret_x1 = t->x;
free(t);
return 0;
}
return -1;
}
static int
ellipseNew(Imaging im, int x0, int y0, int x1, int y1,
const void* ink_, int fill,
int width, int op)
{
DRAW* draw;
INT32 ink;
DRAWINIT();
int a = x1 - x0;
int b = y1 - y0;
if (a < 0 || b < 0) {
return 0;
}
if (fill) {
width = a + b;
}
ellipse_state st;
ellipse_init(&st, a, b, width);
int32_t X0, Y, X1;
while (ellipse_next(&st, &X0, &Y, &X1) != -1) {
draw->hline(im, x0 + (X0 + a) / 2, y0 + (Y + b) / 2, x0 + (X1 + a) / 2, ink);
}
return 0;
}
static int
clipEllipseNew(Imaging im, int x0, int y0, int x1, int y1,
float start, float end,
const void* ink_, int width, int op, clip_ellipse_init init)
{
DRAW* draw;
INT32 ink;
DRAWINIT();
int a = x1 - x0;
int b = y1 - y0;
if (a < 0 || b < 0) {
return 0;
}
clip_ellipse_state st;
init(&st, a, b, width, start, end);
// debug_clip_tree(st.root, 0);
int32_t X0, Y, X1;
int next_code;
while ((next_code = clip_ellipse_next(&st, &X0, &Y, &X1)) >= 0) {
draw->hline(im, x0 + (X0 + a) / 2, y0 + (Y + b) / 2, x0 + (X1 + a) / 2, ink);
}
clip_ellipse_free(&st);
return next_code == -1 ? 0 : -1;
}
static int
arcNew(Imaging im, int x0, int y0, int x1, int y1,
float start, float end,
const void* ink_, int width, int op)
{
return clipEllipseNew(im, x0, y0, x1, y1, start, end, ink_, width, op, arc_init);
}
static int
chordNew(Imaging im, int x0, int y0, int x1, int y1,
float start, float end,
const void* ink_, int width, int op)
{
return clipEllipseNew(im, x0, y0, x1, y1, start, end, ink_, width, op, chord_init);
}
static int
chordLineNew(Imaging im, int x0, int y0, int x1, int y1,
float start, float end,
const void* ink_, int width, int op)
{
return clipEllipseNew(im, x0, y0, x1, y1, start, end, ink_, width, op, chord_line_init);
}
static int
pieNew(Imaging im, int x0, int y0, int x1, int y1,
float start, float end,
const void* ink_, int width, int op)
{
return clipEllipseNew(im, x0, y0, x1, y1, start, end, ink_, width, op, pie_init);
}
static int
pieSideNew(Imaging im, int x0, int y0, int x1, int y1,
float start,
const void* ink_, int width, int op)
{
return clipEllipseNew(im, x0, y0, x1, y1, start, 0, ink_, width, op, pie_side_init);
}
int
ImagingDrawEllipse(Imaging im, int x0, int y0, int x1, int y1,
const void* ink, int fill, int width, int op)
{
return ellipseNew(im, x0, y0, x1, y1, ink, fill, width, op);
}
int
ImagingDrawArc(Imaging im, int x0, int y0, int x1, int y1,
float start, float end, const void* ink, int width, int op)
{
normalize_angles(&start, &end);
if (start + 360 == end) {
return ImagingDrawEllipse(im, x0, y0, x1, y1, ink, 0, width, op);
}
if (start == end) {
return 0;
}
return arcNew(im, x0, y0, x1, y1, start, end, ink, width, op);
}
int
ImagingDrawChord(Imaging im, int x0, int y0, int x1, int y1,
float start, float end, const void* ink, int fill,
int width, int op)
{
normalize_angles(&start, &end);
if (start + 360 == end) {
return ImagingDrawEllipse(im, x0, y0, x1, y1, ink, fill, width, op);
}
if (start == end) {
return 0;
}
if (fill) {
return chordNew(im, x0, y0, x1, y1, start, end, ink, x1 - x0 + y1 - y0 + 1, op);
} else {
if (chordLineNew(im, x0, y0, x1, y1, start, end, ink, width, op)) {
return -1;
}
return chordNew(im, x0, y0, x1, y1, start, end, ink, width, op);
}
}
int
ImagingDrawPieslice(Imaging im, int x0, int y0, int x1, int y1,
float start, float end, const void* ink, int fill,
int width, int op)
{
normalize_angles(&start, &end);
if (start + 360 == end) {
return ellipseNew(im, x0, y0, x1, y1, ink, fill, width, op);
}
if (start == end) {
return 0;
}
if (fill) {
return pieNew(im, x0, y0, x1, y1, start, end, ink, x1 + y1 - x0 - y0, op);
} else {
if (pieSideNew(im, x0, y0, x1, y1, start, ink, width, op)) {
return -1;
}
if (pieSideNew(im, x0, y0, x1, y1, end, ink, width, op)) {
return -1;
}
float xc = round((x0 + x1 - width) / 2.0), yc = round((y0 + y1 - width) / 2.0);
ellipseNew(im, xc, yc, xc + width - 1, yc + width - 1, ink, 1, 0, op);
return pieNew(im, x0, y0, x1, y1, start, end, ink, width, op);
}
}
/* -------------------------------------------------------------------- */
/* experimental level 2 ("arrow") graphics stuff. this implements
portions of the arrow api on top of the Edge structure. the
semantics are ok, except that "curve" flattens the bezier curves by
itself */
struct ImagingOutlineInstance {
float x0, y0;
float x, y;
int count;
Edge *edges;
int size;
};
ImagingOutline
ImagingOutlineNew(void)
{
ImagingOutline outline;
outline = calloc(1, sizeof(struct ImagingOutlineInstance));
if (!outline) {
return (ImagingOutline) ImagingError_MemoryError();
}
outline->edges = NULL;
outline->count = outline->size = 0;
ImagingOutlineMove(outline, 0, 0);
return outline;
}
void
ImagingOutlineDelete(ImagingOutline outline)
{
if (!outline) {
return;
}
if (outline->edges) {
free(outline->edges);
}
free(outline);
}
static Edge*
allocate(ImagingOutline outline, int extra)
{
Edge* e;
if (outline->count + extra > outline->size) {
/* expand outline buffer */
outline->size += extra + 25;
if (!outline->edges) {
/* malloc check ok, uses calloc for overflow */
e = calloc(outline->size, sizeof(Edge));
} else {
if (outline->size > INT_MAX / sizeof(Edge)) {
return NULL;
}
/* malloc check ok, overflow checked above */
e = realloc(outline->edges, outline->size * sizeof(Edge));
}
if (!e) {
return NULL;
}
outline->edges = e;
}
e = outline->edges + outline->count;
outline->count += extra;
return e;
}
int
ImagingOutlineMove(ImagingOutline outline, float x0, float y0)
{
outline->x = outline->x0 = x0;
outline->y = outline->y0 = y0;
return 0;
}
int
ImagingOutlineLine(ImagingOutline outline, float x1, float y1)
{
Edge* e;
e = allocate(outline, 1);
if (!e) {
return -1; /* out of memory */
}
add_edge(e, (int) outline->x, (int) outline->y, (int) x1, (int) y1);
outline->x = x1;
outline->y = y1;
return 0;
}
int
ImagingOutlineCurve(ImagingOutline outline, float x1, float y1,
float x2, float y2, float x3, float y3)
{
Edge* e;
int i;
float xo, yo;
#define STEPS 32
e = allocate(outline, STEPS);
if (!e) {
return -1; /* out of memory */
}
xo = outline->x;
yo = outline->y;
/* flatten the bezier segment */
for (i = 1; i <= STEPS; i++) {
float t = ((float) i) / STEPS;
float t2 = t*t;
float t3 = t2*t;
float u = 1.0F - t;
float u2 = u*u;
float u3 = u2*u;
float x = outline->x*u3 + 3*(x1*t*u2 + x2*t2*u) + x3*t3 + 0.5;
float y = outline->y*u3 + 3*(y1*t*u2 + y2*t2*u) + y3*t3 + 0.5;
add_edge(e++, xo, yo, (int) x, (int) y);
xo = x, yo = y;
}
outline->x = xo;
outline->y = yo;
return 0;
}
int
ImagingOutlineClose(ImagingOutline outline)
{
if (outline->x == outline->x0 && outline->y == outline->y0) {
return 0;
}
return ImagingOutlineLine(outline, outline->x0, outline->y0);
}
int
ImagingOutlineTransform(ImagingOutline outline, double a[6])
{
Edge *eIn;
Edge *eOut;
int i, n;
int x0, y0, x1, y1;
int X0, Y0, X1, Y1;
double a0 = a[0]; double a1 = a[1]; double a2 = a[2];
double a3 = a[3]; double a4 = a[4]; double a5 = a[5];
eIn = outline->edges;
n = outline->count;
/* FIXME: ugly! */
outline->edges = NULL;
outline->count = outline->size = 0;
eOut = allocate(outline, n);
if (!eOut) {
outline->edges = eIn;
outline->count = outline->size = n;
ImagingError_MemoryError();
return -1;
}
for (i = 0; i < n; i++) {
x0 = eIn->x0;
y0 = eIn->y0;
/* FIXME: ouch! */
if (eIn->x0 == eIn->xmin) {
x1 = eIn->xmax;
} else {
x1 = eIn->xmin;
}
if (eIn->y0 == eIn->ymin) {
y1 = eIn->ymax;
} else {
y1 = eIn->ymin;
}
/* full moon tonight! if this doesn't work, you may need to
upgrade your compiler (make sure you have the right service
pack) */
X0 = (int) (a0*x0 + a1*y0 + a2);
Y0 = (int) (a3*x0 + a4*y0 + a5);
X1 = (int) (a0*x1 + a1*y1 + a2);
Y1 = (int) (a3*x1 + a4*y1 + a5);
add_edge(eOut, X0, Y0, X1, Y1);
eIn++;
eOut++;
}
free(eIn);
return 0;
}
int
ImagingDrawOutline(Imaging im, ImagingOutline outline, const void* ink_,
int fill, int op)
{
DRAW* draw;
INT32 ink;
DRAWINIT();
draw->polygon(im, outline->count, outline->edges, ink, 0);
return 0;
}
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