File:Ternary plot visualisation.svg
![File:Ternary plot visualisation.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Ternary_plot_visualisation.svg/512px-Ternary_plot_visualisation.svg.png?20130624000305)
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[edit]DescriptionTernary plot visualisation.svg |
English: Derivation of a ternary plot from Cartesian coordinates:
Figure (1) shows an oblique projection of point P(a,b,c) in a 3-dimensional Cartesian space with axes a, b and c, respectively. If a + b + c = K (a positive constant), P is restricted to a plane containing A(K,0,0), B(0,K,0) and C(0,0,K). If a, b and c each cannot be negative, P is restricted to the triangle bounded by A, B and C, as in (2). In (3), the axes are rotated to give an isometric view. The triangle, viewed face-on, appears equilateral. In (4), the distances of P from lines BC, AC and AB are denoted by a' , b' and c' , respectively. For any line l = s + t n̂ in vector form (n̂ is a unit vector) and a point p, the distance from a point to a line from p to l is In this case, point P is at
Line BC has
Using the perpendicular distance formula,
Substituting K = a + b + c,
Similar calculation on lines AC and AB gives
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Source | Own work |
Author | Cmglee |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 00:03, 24 June 2013 | ![]() | 512 × 128 (5 KB) | Cmglee (talk | contribs) | Fix svg viewBox. |
00:01, 24 June 2013 | ![]() | 512 × 512 (5 KB) | Cmglee (talk | contribs) | Finish graphic. | |
19:58, 21 June 2013 | ![]() | 512 × 154 (6 KB) | Cmglee (talk | contribs) | {{Information |Description ={{en|1=Derivation of ternary plots from Cartesian coordinates: For a line '''l''' = '''s''' + ''t'' '''n''' in vector form, where '''n''' is a unit vector, and a point '''p''', the [[distance from a point to a line|perp... |
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Short title | Derivation of ternary plots from Cartesian coordinates |
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Image title | Derivation of ternary plots from Cartesian coordinates, drawn by CMG Lee. (1) shows a point P(a,b,c) in a 3-dimensional Cartesian plane. In (2), if a + b + c = K, and a, b and c are non-negative, P is restricted to the triangle bounded by A, B and C. In (3), the axes are rotated to give an isometric view (the triangle appears equilateral). In (4), the distances of P from lines BC, AC and AB are denoted by a', b' and c'. |
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Height | 100% |