Difference between revisions of "Trilinear Command"
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{{command|geometry}} | {{command|geometry}} | ||
| − | ;Trilinear[<Point A>,<Point B>,<Point C>,<Number | + | ;Trilinear[<Point A>,<Point B>,<Point C>,<Number u>, <Number v>, <Number w>] |
| − | :creates point whose [[w:Trilinear coordinates|trilinear coordinates]] with respect to triangle ''ABC'' are ''( | + | :creates point whose [[w:Trilinear coordinates|trilinear coordinates]] with respect to triangle ''ABC'' are ''(u,v,w)''. |
| + | |||
| + | |||
| + | ==Some examples : == | ||
| + | <center> | ||
| + | {| class="wikitable" style="text-align:center;" | ||
| + | |- | ||
| + | ! Point !! u !! v !! w | ||
| + | |- | ||
| + | ! A | ||
| + | || 1 || 0 || 0 | ||
| + | |- | ||
| + | ! B | ||
| + | || 0 || 1 || 0 | ||
| + | |- | ||
| + | ! C | ||
| + | || 0 || 0 || 1 | ||
| + | |- | ||
| + | ! CircumCenter | ||
| + | || cos(<math>\hat{A}</math>) || cos(<math>\hat{B}</math>) || cos(<math>\hat{C}</math>) | ||
| + | |- | ||
| + | ! Center of Incircle | ||
| + | || 1 || 1 || 1 | ||
| + | |- | ||
| + | !Center of excircle tangent to [BC] | ||
| + | ||-1||1||1 | ||
| + | |- | ||
| + | !Center of excircle tangent to [AC] | ||
| + | ||1||-1||1 | ||
| + | |- | ||
| + | !Center of excircle tangent to à [AB] | ||
| + | ||1||1||-1 | ||
| + | |- | ||
| + | ! Centroid | ||
| + | || <math>\frac{1}{a}</math> || <math>\frac{1}{b}</math> || <math>\frac{1}{c}</math> | ||
| + | |- | ||
| + | ! Orthocenter | ||
| + | || cos(<math>\hat{B}</math>) cos(<math>\hat{C}</math>) || cos(<math>\hat{A}</math>) cos(<math>\hat{C}</math>) || cos(<math>\hat{A}</math>)cos(<math>\hat{B}</math>) | ||
| + | |} | ||
| + | </center> | ||
Revision as of 13:13, 17 February 2013
- Trilinear[<Point A>,<Point B>,<Point C>,<Number u>, <Number v>, <Number w>]
- creates point whose trilinear coordinates with respect to triangle ABC are (u,v,w).
Some examples :
| Point | u | v | w |
|---|---|---|---|
| A | 1 | 0 | 0 |
| B | 0 | 1 | 0 |
| C | 0 | 0 | 1 |
| CircumCenter | cos(\hat{A}) | cos(\hat{B}) | cos(\hat{C}) |
| Center of Incircle | 1 | 1 | 1 |
| Center of excircle tangent to [BC] | -1 | 1 | 1 |
| Center of excircle tangent to [AC] | 1 | -1 | 1 |
| Center of excircle tangent to à [AB] | 1 | 1 | -1 |
| Centroid | \frac{1}{a} | \frac{1}{b} | \frac{1}{c} |
| Orthocenter | cos(\hat{B}) cos(\hat{C}) | cos(\hat{A}) cos(\hat{C}) | cos(\hat{A})cos(\hat{B}) |
