差分
このページの2つのバージョン間の差分を表示します。
| 次のリビジョン | 前のリビジョン | ||
| research:memos:mathematics:2d_notes [2017/12/18 02:01] – 作成 kobayash | research:memos:mathematics:2d_notes [2017/12/18 04:52] (現在) – kobayash | ||
|---|---|---|---|
| 行 1: | 行 1: | ||
| - | ===== Notes ===== | + | ===== 2D notes ===== |
| + | ==== Intersection of two lines ==== | ||
| + | \begin{align} | ||
| + | \left\{ | ||
| + | \begin{array}{l} | ||
| + | y = a_1x+b_1 \\ | ||
| + | y = a_2x+b_2 | ||
| + | \end{array} | ||
| + | \right. | ||
| + | \end{align} | ||
| + | If $a_1 \ne a_2$, | ||
| + | \begin{align} | ||
| + | \left\{ | ||
| + | \begin{array}{l} | ||
| + | x = -\dfrac{b_2-b_1}{a_2-a_1} \\ | ||
| + | y = \dfrac{a_2b_1-a_1b_2}{a_2-a_1} | ||
| + | \end{array} | ||
| + | \right. | ||
| + | \end{align} | ||
| + | |||
| + | ==== A line between two points ==== | ||
| + | \begin{align} | ||
| + | \left\{ | ||
| + | \begin{array}{l} | ||
| + | y_1 = ax_1+b \\ | ||
| + | y_2 = ax_2+b | ||
| + | \end{array} | ||
| + | \right. | ||
| + | \end{align} | ||
| + | If $x_1 \ne x_2$, | ||
| + | \begin{align} | ||
| + | \left\{ | ||
| + | \begin{array}{l} | ||
| + | a=\dfrac{y_2-y_1}{x_2-x_1}\\ | ||
| + | b=\dfrac{x_2y_1-x_1y_2}{x_2-x_1} | ||
| + | \end{array} | ||
| + | \right. | ||
| + | \end{align} | ||
