一個圓周計算的問題 |
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尚未結案
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harisan3
一般會員   發表：6 回覆：11 積分：3 註冊：2004-12-10 發送簡訊給我 |
void MakeEllipticalOutline(OUTLINE *outline, int xrad, int yrad)
{
short *ptr;
float *ptrn;
int xradsq = xrad * xrad;
int yradsq = yrad * yrad;
double ratio = ((double) xradsq) / ((double) yradsq);
int xradbkpt = (int) (xradsq / sqrt((double) xradsq yradsq));
int yradbkpt = (int) (yradsq / sqrt((double) xradsq yradsq));
int x, y; // x & y are in image coordinates
int curx, cury; // count # of iterations in loops below
outline->perim_length = 4 * xradbkpt 4 * yradbkpt 4;
outline->perim = (short *)
malloc(2 * (outline->perim_length) * sizeof(short));
outline->normals = (float *)
malloc(2 * (outline->perim_length) * sizeof(float));
ptr = outline->perim;
ptrn = outline->normals;
*(ptr) = curx = 0; // perimeter starts at top and proceeds clockwise
*(ptr) = cury = - yrad;
*ptrn = 0.0f;
*ptrn = -1.0f; // from 0 to 45 degrees, measured cw from top
for (x = 1; x <= xradbkpt ; x ) {
y = (int) (-yrad * sqrt(1 - ((double) x / xrad)*((double) x / xrad)));
*(ptr) = x - curx;
*(ptr) = y - cury;
*ptrn = (float) ( x / sqrt(x*x ratio*y*y));
*ptrn = (float) ((ratio*y) / sqrt(x*x ratio*y*y));
curx = x;
cury = y;
}
// from 45 to 135 degrees (including right axis)
for (y = - yradbkpt ; y <= yradbkpt ; y ) {
x = (int) (xrad * sqrt(1 - ((double) y / yrad)*((double) y / yrad)));
*(ptr) = x - curx;
*(ptr) = y - cury;
*ptrn = (float) ( x / sqrt(x*x ratio*y*y));
*ptrn = (float) ((ratio*y) / sqrt(x*x ratio*y*y));
curx = x;
cury = y;
}
// from 135 to 225 degrees (including down axis)
for (x = xradbkpt ; x >= - xradbkpt ; x--) {
y = (int) (yrad * sqrt(1 - ((double) x / xrad)*((double) x / xrad)));
*(ptr) = x - curx;
*(ptr) = y - cury;
*ptrn = (float) ( x / sqrt(x*x ratio*y*y));
*ptrn = (float) ((ratio*y) / sqrt(x*x ratio*y*y));
curx = x;
cury = y;
}
// from 225 to 315 degrees (including left axis)
for (y = yradbkpt ; y >= - yradbkpt ; y--) {
x = (int) (-xrad * sqrt(1 - ((double) y / yrad)*((double) y / yrad)));
*(ptr) = x - curx;
*(ptr) = y - cury;
*ptrn = (float) ( x / sqrt(x*x ratio*y*y));
*ptrn = (float) ((ratio*y) / sqrt(x*x ratio*y*y));
curx = x;
cury = y;
}
// from 315 to 360 degrees
for (x = - xradbkpt ; x < 0 ; x ) {
y = (int) (-yrad * sqrt(1 - ((double) x / xrad)*((double) x / xrad)));
*(ptr) = x - curx;
*(ptr) = y - cury;
*ptrn = (float) ( x / sqrt(x*x ratio*y*y));
*ptrn = (float) ((ratio*y) / sqrt(x*x ratio*y*y));
curx = x;
cury = y;
}
outline->halfsize_x = xrad;
outline->halfsize_y = yrad;
outline->area = MakeMask(outline);
}
請問個數學問題,為什麼圓周上面的點的算法會變成下面的寫法?
// from 0 to 45 degrees, measured cw from top
for (x = 1; x <= xradbkpt ; x ) {
y = (int) (-yrad * sqrt(1 - ((double) x / xrad)*((double) x / xrad)));
我帶數學公式還是無法理解,請各位數學比較好的幫幫我解釋一下,感恩喔.
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spruce
一般會員 發表：3 回覆：11 積分：2 註冊：2005-11-05 發送簡訊給我 |
發表時間：2005-10-27 16:13:08
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系統時間：2024-04-19 20:18:32
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