SVG path tracer des courbes

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Comment tracer des courbes


HTML5 cours tutorial SVG

En général, une courbe de Bézier est une expression polynomiale, utilisée pour décrire une courbe.
Ils sont couramment utilisés dans les logiciels d'infographie, mais ils ne peuvent toujours être appelés quelque chose de plus qu'une courbe.
Généralement, l'utilisateur sélectionne deux points qui representent les deux bouts de la courbe et un ou deux points de contrôle.
Une courbe de Bézier avec un point control s'appelle une courbe de Bézier quadratique et le genre avec deux points de contrôle est appelé cube.

Dessiner  les courbes de Bézier quadratiques en SVG

Les commandes Bézier quadratique sont (Q, q, T et t)

La commande Q OU q

Pour tracer des courbes de Bézier quadratiques il faut trois paramêtres: un point de départ, un point d’arrivée et un point de contrôle.
On commence d’abord par tracer un segment puis on place le point de contrôle, qu’on appele point d’inflexion.
La lettre qui désigne cette commande est Q. Elle peut évidemment être écrite en minuscule, ce qui signifiera que les coordonnées indiquées sont relatives.
 Cette commande requiert deux paramètres et donc quatre nombres/: les coordonnées du point d’inflexion et les coordonnées du point d’arrivée.
En SVG, le point de départ est donné par la commande précédente.

Sélectionner le code


  <!DOCTYPE html>
 <html>
 <head>
 <title> SVG tracer des courbes</title>
 <meta charset="UTF-8">
 <style>
 #blue{
      stroke:blue;
      stroke-width:4;
      fill:none;
      }      
 #red{
      stroke:red;
      stroke-width:4;
      fill:none;
      }      
     
 </style>
 </head>
 <body>
 <div>
 <svg viewBox="0 0 1200 700" xmlns="http://www.w3.org/2000/svg"
  version="1.1">
      <path  d = "M 50,200 Q100,10 350,200" id="blue"/>
 <path  d = "M 50,200 Q500,10 350,200"  id="red"/>
     
      <g stroke = "black" stroke-width = "2" fill =
  "black">
     <circle id = "pointA" cx = "50" cy = "200" r =
  "2"/>
     <circle id = "pointB" cx = "100" cy = "10" r =
  "2"/>
     <circle id = "pointC" cx = "350" cy = "200" r =
  "2"/>
     <circle id = "pointD" cx = "500" cy = "10" r =
  "2"/>
 </g>
      <g font-size = "20" font = "sans-serif" fill =
  "black" stroke = "none" text-anchor = "middle">
     <text x = "50" y = "200" dx = "-30">
         A
     </text>
     <text x = "100" y = "10" dx = "-20" dy = "20">
         B
     </text>
     <text x = "350" y = "200" dx = "20" dy = "20">
         C
     </text>
     <text x = "500" y = "20" dy = "20" >
         D
     </text>
    
 </g>
      <g style="stroke:rgb(0,255,0);stroke-width:1">
        <line x1="50" y1="200" x2="100" y2="10"/>
        <line x1="350" y1="200" x2="100" y2="10"/>
        <line x1="50" y1="200" x2="500" y2="10"/>
        <line x1="350" y1="200" x2="500" y2="10"/>
      </g>
 </svg>
  </div>
 </body>
 </html>

 

Voici le résultat :
courbes de Bézier quadratiques
Dans l’exemple j’ai mis des tracés pour deux courbes de couleur différentes avec le même point de départ A 50,200 est le même point d’arrivé C 350,200 et en fin chaque courbe a un point de contrôle  la courbe bleu avec comme point de contrôle B 100,10 et la courbe rouge avec comme point de contrôle D 500,10 .
Cet exemple montre que plus les points de la courbe sont plus proche du point de contrôle plus ils sont étirées vers celui-ci et déformés. On a l’impression que le point de contrôle est comme un aimant.

La commande T OU t

La commande T peut être définit comme une commande complémentaire de la commande Q.
La commande T ne trace pas une nouvelle courbe, elle ne fait que continue la courbe qui la précéde.
La commande T nécessite un seul point qui sera le point d’arrivé, le point de départ est le point d’arrivé de la courbe précédente et le point de contrôle est le point symétrique du point de contrôle de la courbe précédente.
Exemple :

Sélectionner le code


  <!DOCTYPE html>
 <html>
 <head>
 <title> SVG dessiner des courbes</title>
 <meta charset="UTF-8">
 <style>
 path{fill:none;stroke:#0000ff;stroke-width:4;}  
 </style>
 </head>
 <body>
 <div>
 <svg viewBox="0 0 1200 700" xmlns="http://www.w3.org/2000/svg"
  version="1.1">
       <path  d ="M 50,200 Q100,10 350,200 T650,200" />
 </svg>
  </div>
 </body>
 </html>

 

Dessiner  les courbes de Bézier cubique en SVG la commande C

Les courbes de Bézier cubiques sont un peu plus difficiles à obtenir que quadratiques.
Quatre points A, B, C et D dans le plan ou dans un espace tridimensionnel sont nécessaires pour définir une courbe de Bézier cubique.
La courbe commence à A se déplace vers B pour arrive à D venant de la direction de C.
En général, la corbe ne passera pas par B ou C ; ces points sont là uniquement pour fournir des informations directionnelles.
La distance entre A et B déterminent « le temps » que la courbe va faire en se déplaçant dans la direction B avant de tourner vers D.
Dans l'exemple ci-dessous, la courbe à la gauche a deux points de contrôle là où l'exemple précédent avait un seul. 
La courbe du milieu a les points de contrôle répartis 50 unités à droite et à gauche du point précédent. 
La courbe de la droite utilise les mêmes points de contrôle que la courbe du milieu, mais leur ordre est inversé.  
Exemple

Sélectionner le code


  <!DOCTYPE html>
 <html>
 <head>
 <title> SVG utilisation du path</title>
 <meta charset="UTF-8">
 </head>
 <body>
 <div>
 <svg viewBox="0 0 1200 700" xmlns="http://www.w3.org/2000/svg"
  version="1.1">
  <!-- les courbes -->
 <path d = "M 100 350 c 150 -300 150 -300 300 0" stroke =
  "red" stroke-width = "5" fill = "none"/>
 <path d = "M 450 350 c 200 -300 100 -300 300 0" stroke =
  "blue" stroke-width = "5" fill = "none"/>       
 <path d = "M 800 350 c 100 -300 200 -300 300 0" stroke =
  "green" stroke-width = "5" fill = "none"/>
  <!-- les étiquettes  -->  
    <g  stroke-width = "3">
     <!-- deux points de contrôle identiques -->
     <circle cx = "250" cy = "50" r = "3" fill = "red"/>
     <!-- deux points de contrôle -->
     <circle cx = "650" cy = "50" r = "3" fill =
  "blue"/>
     <circle cx = "550" cy = "50" r = "3" fill =
  "blue"/>
     <!-- deux points de contrôle -->
     <circle cx = "900" cy = "50" r = "3" fill =
  "green"/>
     <circle cx = "1000" cy = "50" r = "3" fill =
  "green"/>
               
 </g>
      <g font-size = "16" font = "sans-serif" stroke =
  "none">
      <text x = "100" y = "400" dy = "-10" fill ="red" >
      Courbe avec deux points de contrôle identiques
 </text>
      <text x = "450" y = "400" dy = "-10" fill ="blue"
  >
      Courbe avec deux points de contrôle identiques
 </text>
                <text x = "800" y = "400" dy = "-10" fill
  ="green" >
      Courbe avec deux points de contrôle identiques
 </text>
      </g>
 <g font-size = "30" font = "sans-serif" fill = "black"
  stroke = "none" text-anchor = "middle">
     <text x = "250" y = "50" dy = "-10">
        PC 1 et 2
     </text>
     <text x = "650" y = "50" dy = "-10">
         PC1
     </text>
     <text x = "550" y = "50" dy = "-10">
         PC2
     </text>
     <text x = "900" y = "50" dy = "-10">
         PC2
     </text>
     <text x = "1000" y = "50" dy = "-10">
         PC1
     </text>
 </g>
 </svg>
  </div>
 </body>
 </html>

 

Voici le résultat :
courbes de Bézier cubique en SVG la commande C

La commande S

Vous en doutez que comme pour la commande Q et La commande T, il y a aussi pour la commande C une commande qui la complète en douceur. Et bien oui c’est la commande S.
La commande S prend non pas une mais deux paires de coordonnées donc deux point, le premièr point est le second point de contrôle et le second est le point d’arrivé.
 Le premier point d’inflexion est calculé à partir de la commande précédente, qui doit être obligatoirement une commande de courbe de Bézier cubique, soit une commande C ou une commande S.
Exemple :
 

Sélectionner le code


  <!DOCTYPE html>
 <html>
 <head>
 <title> SVG tracer des courbes</title>
 <meta charset="UTF-8">
 <style>
 path{fill:none;stroke:#0000ff;stroke-width:4;}  
 </style>
 </head>
 <body>
 <div>
 <svg viewBox="0 0 1200 700" xmlns="http://www.w3.org/2000/svg"
  version="1.1">
  <path d = "M 450,350 C650,50 100,300 650,300 S200,300 650,100
  "/>
 </svg>
  </div>
 </body>
 </html>

 

Les arcs elliptiques la commande A

Un arc elliptique est une partie d’ellipse.
La commande nécessaire pour tracer un arc elliptique est la commande A.
Pour un arc elliptique il nous faut sept paramètres comme suit :
1 - La longueur du rayon x.
2 - La longueur du rayon y.
3 - La rotation en degrés de l’axe x de l’ellipse par rapport à l’axe des ordonnées.Cette rotation a le sens inverse des aiguilles d’une montre.
4 - Un paramètre, qui indique si la mesure de l’arc fait plus de la moitié du périmètre de l’ellipse (valeur : 1), ou  fait moins de la moitié du périmètre (valeur/: 0).
5 - Un paramètre, qui  indique si l’arc doit être dessiné dans la direction négative des angles (valeur : 0) ou dans la direction positive des angles (valeur/: 1).
 Les deux derniers sont les coordonnées du point d’arrivée, les coordonnées du point de départ étant données par la commande précédent à la commande A.
Exemple :
 

Sélectionner le code


  <!DOCTYPE html>
 <html>
 <head>
 <title> SVG tracer des courbes</title>
 <meta charset="UTF-8">
 <style>
 path{fill:none;stroke:#0000ff;stroke-width:4;}  
 </style>
 </head>
 <body>
 <div>
 <svg viewBox="0 0 1200 700" xmlns="http://www.w3.org/2000/svg"
  version="1.1">
       <path d = "M10,50A50 20 0 0 0 110,50 "/>
       <path d = "M310,50a50 20 0 0 1 110,50 "/>
 </svg>
  </div>
 </body>
 </html>

 

Et voilà !!!
Mais avant de terminer avec cette partie j’aimerais vous donner des exemples créer à l’aiddule du logiciel de dessin spécialisé en SVG,  Inkscape.

Exemple 1 dessin d’une fleur simple

Sélectionner le code


  <!DOCTYPE html>
 <html>
 <head>
 <title> SVG dessiner fleur</title>
 <meta charset="UTF-8">
 <style>
 path{fill:#800080;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.51783937;stroke-linecap:butt;stroke-linejoin:miter;marker:none;marker-start:none;marker-mid:none;marker-end:none;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;visibility:visible;display:inline;overflow:visible;enable-background:accumulate}
     
 </style>
 </head>
 <body>
 <div>
 <svg viewBox="-140 -40 1200 700"
  xmlns="http://www.w3.org/2000/svg" version="1.1">
   <g>
 <path d="M 118.76598,214.16484 C 338.93037,15.927925
  -191.40674,439.09593 104.44766,454.60101 C 400.30207,470.10608
  -82.896709,-6.1790943 115.3402,213.9853 C 313.57712,434.1497
  -109.59089,-96.187418 -125.09596,199.66698 C -140.60103,495.52139
  335.68414,12.322613 115.51974,210.55953 C -104.64465,408.79644
  425.69246,-14.371569 129.83806,-29.876641 C -166.01634,-45.381712
  317.18243,430.90346 118.94552,210.73906 C -79.291398,-9.4253314
  343.87661,520.91178 359.38168,225.05738 C 374.88676,-70.797023
  -101.39842,412.40175 118.76598,214.16484 z " />
   </g>
 </svg>
 </div>
 </body>
 </html>

 

Exemple 2 Dessin d’une vache :

Sélectionner le code


  <!DOCTYPE html>
 <html>
 <head>
 <title> SVG dessin de vache</title>
 <meta charset="UTF-8">
 <style>      
 </style>
 </head>
 <body>
 <div>
 <svg xmlns="http://www.w3.org/2000/svg"
  xmlns:xlink="http://www.w3.org/1999/xlink"
  xmlns:svg="http://www.w3.org/2000/svg"
  xmlns:dc="http://purl.org/dc/elements/1.1/"
  xmlns:cc="http://web.resource.org/cc/"
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  version="1.1" width="200"  viewBox="0 0 540.869 384.938"
  overflow="visible">
 <g>
     
      <path  fill="Sienna"
  d="M87.392,12.646c2.565,3.435,5.977,6.023,9,9l-0.5,1.5l0.5,1.5  
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  c1.163,0.163,1.779-0.221,2-1l1,0.5l1,0.5c3.288,0.664,2.392,3.957,6,2c-2.274,0.726,0.921,6.921-3,6c-0.1,3.1,0.453,5.547,2,7  
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  l1.5-0.5c-0.908,3.278-7.426,8.698-2,12c2.034-4.008,3.646-5.208,6-7c-2.195-2.295,1.526-4.295-2-6c4.239-1.095,2.674-7.992,6-10  
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  l1.5,0.5l-0.5-1.5c2.689,0.689,1.933-2.067,3-3l1.5-0.5l-0.5-1.5c5.009-0.324,6.202-4.465,10-6c-10,6-11.5,6.5-11.5,6.5l0.5,1.5  
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  l-1.167,1.5c-2.882,0.451-3.128,3.539-7,3l0.5-1.5l-1.5-0.5c2.687-9.98,9.727-15.606,14-24l1.5,0.5l0.5-1.5  
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   c-2.072,0.595-6.569-1.236-7,1c2.833,1.042,4.167,1.042,7,0l1.5,0.5l-0.5-1.5c3.19,0.857,3.093-1.574,5-2h1V44.646z
  M63.392,58.646  
  c0.667,0,1.333,0,2,0c0.61-0.057,1.184-0.149,1-1c-1.322-0.012-0.914-1.753-2-2C64.435,57.022,63.921,57.842,63.392,58.646z   
  M76.392,59.646c1.542-3.019-5.174-2.631-5-1C73.71,58.327,75.231,58.807,76.392,59.646z
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  c-1.086-0.247-0.678-1.988-2-2c-0.323,7.728-7.355,22.127-4,28c-0.541-0.946,0.523-1.952,1-2v1h1c1.869-1.958,3.663-0.309,6,0  
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  l0.5,1c0,0.667,0,1.333,0,2c2.279,0.279,3.759-0.241,4-2l1.5-0.5l-0.5-1.5c20.848,0.761,39.019-0.047,58,1l-0.5,1.5l1.5,0.5  
  c-7.2,4.133-9.854,12.813-11,23c-6.953,1.742-11.165,10.335-19,8c-5.993,6.053-0.55,13.243,3,18c1.363,8.392-6.469,19.154-1,24  
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      <path
  d="M74.892,7.146l-1.5-0.5c0-0.667,0-1.333,0-2l1.5,0.5l0.5-1.5  
  c5.322-1.615,4.508,4.867-1,5L74.892,7.146z"/>
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  d="M120.392,137.646c0.543-1.124,0.447-2.887,0.5-4.5"/>
                <path    stroke-width="1.2247"
  d="M125.892,115.146c-0.058-1,0.457-2,1-3"/>
                <path    stroke-width="1.8105"
  d="M141.892,214.146c1.733,3.836,5.794,4.562,8.143,7.714"/>
                <path    stroke-width="2.1602"
  d="M457.392,255.146c0.06-0.667,0.276-1.333,0.5-2"/>
                <path    stroke-width="2.2211"
  d="M459.892,245.146c1.584-2.611,2.911-5.209,4-8"/>
                <path    stroke-width="2.0449"
  d="M396.892,273.146c-0.729-1.92-3.425-1.734-4-4"/>
      </g>
 </g>
 </svg>
  </div>
 </body>
 </html>

 

Ressources :
Voici un lien qui donne plusieurs cliparts en SVG : http://openclipart.org/

Par carabde 20 Avril 2014