由 --- 於 星期一 七月 07, 2003 9:21 pm
(**) 線ㄉ公式:
(1) Slope y-intercept form:
斜截式
y = m x + b, if m is finite.
(2) Two point form:
兩點式
(x-x1)(y2-y1) = (y-y1)(x2-x1).
(3) Point slope form:
點斜式
y - y1 = m(x-x1), if m is finite.
(4) Intercept form:
截距式
x/a + y/b = 1, if neither a nor b is zero.
(5) Normal form:
法向式
x cos(omega) + y sin(omega) = p.
(6) Parametric form:
參數式
x = x1 + t cos(alpha),
y = y1 + t sin(alpha),
where t is any real number.
(7) Point direction form:
點向式
(x-x1)/A = (y-y1)/B,
where (A,B) is the direction of the line and P1 lies on the line.
(8) General form:
一般式
A x + B y + C = 0,
where A, B, and C are real numbers, and not both A and B are zero.
(**) 點線距離:
The distance from Ax + By + C = 0 to P1 is
d = (Ax1+By1+C)/sqrt(A2+B2).
(**) 兩線交點:
If A1x + B1y + C1 = 0 and A2x + B2y + C2 = 0 are two lines, then their slopes are given by m1 = -A1/B1 and m2 = -A2/B2.
If they intersect, their intersection point has coordinates
x = (-C1B2+C2B1)/(A1B2-A2B1), y = (-A1C2+A2C1)/(A1B2-A2B1).
(**) 3 線共交點:
A1x + B1y + C1 = 0,
A2x + B2y + C2 = 0,
A3x + B3y + C3 = 0,
are concurrent (that is, all pass through a single point) if and only if the determinant
| A1 B1 C1 |
| A2 B2 C2 |= 0.
| A3 B3 C3 |