File:A code snippet for a rhombic repetitive pattern.svg
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Summary
| Description |
English: A rectangular repetitive pattern becomes the rhombic pattern of the SVG image, through the following code snippet: 'patternTransform= "translate(42,147) scale(1.035) rotate(-15) skewX(-30)"' . This composition of four transformations can be coded "matrix(1 -.2679 -.3094 1.1547 42 147)" , where the last two integers are the coordinates of the translation. The first four numbers come out the product of the following matrices, which represent 'scale(1.035) rotate(-15)' and 'skewX(-30)' : | 1 tan 15°| | 1 – tan 30°| | – tan 15° 1 | | 0 1 | The sequence '1 -.2679 -.3094 1.1547' is used in the source code of other SVG images, with an initial rectangular pattern of same dimensions: width="336" height="291" . In the source code of the following images there is also the sequence '1 -.2679 -.3094 1.1547' . The following SVG images also transform a rectangle into a rhombus, to show a periodic tiling by regular polygons: triangles and hexagons. However, in these tilings, a common boundary of two adjoining tiles is not a full edge of the two tiles. Just before the closing </pattern>, "M224 0 336 97V0m0 291V194H224v97M0 0V97H112V0M0 194v97H112" represents four semi-transparent surfaces: two rectangles and two right triangles. Each triangle is one half of a rectangle. Because of 'skewX(-30)' , we see two rhombi instead of two rectangles and two equilateral triangles instead of two right triangles. In order to study the source code and the present description, here are some numbers.tan 15 o = 2 – √3 ; 1 / cos 15 o ≈ 1.035 ; 56 × tan 15 o ≈ 15 ; 336 = 6 × 56 ; 56 × √3 ≈ 97 ; 3 × 97 = 291 ; (112 ; –30 ) + (–30 ; 112) = ( 82 ; 82 ) ; (42 ; 147 ) + 6 × ( 82 ; 82 ) = (534 ; 639). Français : Un motif répétitif rectangulaire devient le motif en forme de losange de l’image SVG, grâce à l’extrait de code suivant : 'patternTransform= "translate(42,147) scale(1.035) rotate(-15) skewX(-30)"' . Cette composition de quatre transformations peut se coder "matrix(1 -.2679 -.3094 1.1547 42 147)" , où les deux derniers nombres entiers sont les coordonnées de la translation. Les quatre premiers nombres résultent du produit des matrices suivantes, qui représentent 'scale(1.035) rotate(-15)' et 'skewX(-30)' : | 1 tan 15°| | 1 – tan 30°| | – tan 15° 1 | | 0 1 | La suite '1 -.2679 -.3094 1.1547' est utilisée dans le code source d’autres images SVG, avec un motif rectangulaire initial de mêmes dimensions : width="336" height="291" . Dans le code source des images suivantes il y a aussi la suite '1 -.2679 -.3094 1.1547' . Les images SVG suivantes transforment aussi un rectangle en un losange, pour montrer un pavage périodique par des polygones réguliers, triangulaires et hexagonaux. Toutefois, dans ces pavages, la frontière commune de deux éléments adjacents n’est pas le bord complet des deux éléments. Juste avant la balise de fermeture </pattern>, "M224 0 336 97V0m0 291V194H224v97M0 0V97H112V0M0 194v97H112" représente quatre surfaces semi-transparentes : deux rectangles et deux triangles rectangles. Chaque triangle est une moitié de rectangle. À cause de 'skewX(-30)' , on voit deux losanges au lieu de deux rectangles, et deux triangles équilatéraux au lieu de deux triangles rectangles. Afin d’étudier le code source et la description présente, voici quelques nombres.tan 15 o = 2 – √3 ; 1 / cos 15 o ≈ 1.035 ; 56 × tan 15 o ≈ 15 ; 336 = 6 × 56 ; 56 × √3 ≈ 97 ; 3 × 97 = 291 ; (112 ; –30 ) + (–30 ; 112) = ( 82 ; 82 ) ; (42 ; 147 ) + 6 × ( 82 ; 82 ) = (534 ; 639). |
| Date | |
| Source | Own work |
| Author | Baelde |
| Other versions |
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| SVG development |  This /Baelde was created with a text editor. |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:26, 13 June 2013 | | 600 × 600 (1 KB) | Baelde | User created page with UploadWizard |
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