2c:null 2d:["$","title",null,{"children":"Analyse comparative entre les distorsions des projections geoPylmyst, geoEquirectangular et geoMollweide | linard-y | Observable"}] 32:T476,md`Pour N points P(${tex`\lambda`}, ${tex`\varphi`}) répartis uniformément sur le globe, considérons un surface élémentaire ${tex`dS = r.cos(\varphi)d\lambda \times r.d\varphi)`}. En considérant ${tex`d\lambda = \epsilon/cos(\varphi)`} et ${tex`d\varphi = \epsilon`}, il nous vient ${tex`dS = r^2\epsilon^2`}. Nous calculons la distorsion surfacique comme le logarythme du rapport de l'aire projetée de l'élément de surface défini par les 4 points du globe [P(${tex`\lambda`}, ${tex`\varphi`}), P${tex`_1`}(${tex`\lambda`} + ${tex`\epsilon`}, ${tex`\varphi`}]), P${tex`_2`}(${tex`\lambda`}, ${tex`\varphi`} + ${tex`\epsilon`}/cos(${tex`\varphi`})), P${tex`_3`}(${tex`\lambda`} + ${tex`\epsilon`}, ${tex`\varphi`} + ${tex`\epsilon`}/cos(${tex`\varphi`}))] et de l'aire ${tex`r^2\epsilon^2`} associée au point P(${tex`\lambda`}, ${tex`\varphi`}) considéré. Chaque distorsion surfacique est ensuite normalisée en divisant par la distorsion calculée à un point de référence que l'on choisi comme étant le point [25.163, 8.903] (centroïde de la face 3 du développement de l'icosaèdre utilisé par la projection geoPylmyst).`33:T749,AREA = { const map1 = mapfillContours( p => { const c = distorsion(p, projection1).area / ref(projection1); return c > 1 ? c - 1 : 1 - 1 / c; }, points, projection1, { width:2*dim1[0], height:2*dim1[1], margins:[6,6], land:[land], fill: colorArea } ) let ctx1 = map1.getContext("2d"); ctx1.beginPath(); d3.geoPath(projection1, ctx1).pointRadius(4)({type:"Point", coordinates: refPoint}); ctx1.strokeStyle = "#000"; ctx1.fillStyle = "red"; ctx1.stroke(); ctx1.fill(); ///// const map2 = mapfillContours( p => { const c = distorsion(p, projection2).area / ref(projection2); return c > 1 ? c - 1 : 1 - 1 / c; }, points, projection2, { width:2*dim2[0], height:2*dim2[1], land:[land], fill: colorArea } ) let ctx2 = map2.getContext("2d"); ctx2.beginPath(); d3.geoPath(projection2, ctx2).pointRadius(4)({type:"Point", coordinates: refPoint}); ctx2.strokeStyle = "#000"; ctx2.fillStyle = "red"; ctx2.stroke(); ctx2.fill(); ///// const map3 = mapfillContours( p => { const c = distorsion(p, projection3).area / ref(projection3); return c > 1 ? c - 1 : 1 - 1 / c; }, points, projection3, { width:2*dim3[0], height:2*dim3[1], land:[land], fill: colorArea } ) let ctx3 = map3.getContext("2d"); ctx3.beginPath(); d3.geoPath(projection3, ctx3).pointRadius(4)({type:"Point", coordinates: refPoint}); ctx3.strokeStyle = "#000"; ctx3.fillStyle = "red"; ctx3.stroke(); ctx3.fill(); return html`${map1}${map2}${map3}`; }34:T52a,function mapfillContours(valuePoint, points, projection, options) { let opts = Object.assign({ width: 960, height: 480, fill : d3.scaleLinear().range(["orange", "lime"]), land: [], margins: [6, 6], thresholds: 100 }, options); const extent = ({width:opts.width+2*opts.margins[0], height:opts.height+2*opts.margins[1]}); const contours = getContours(valuePoint, points, opts); const context = DOM.context2d(extent.width, extent.height); var path = d3.geoPath(projection, context); canvasSetBackground(context, extent.width, extent.height, {fill:"#000"}); canvasClipSphere(context, projection); canvasDrawSphere(context, projection, {fill: "#fff"}); if (contours.isobands(points)!=undefined) { for (const c of contours.isobands(points)) { rearrange(c.coordinates); context.beginPath(); path(c); context.strokeStyle = context.fillStyle = opts.fill((c.value + c.valueMax) / 2); context.fill(); context.stroke(); } } else { canvasDrawSphere(context, projection, {fill:"white"}); } canvasDrawLand(context, projection, opts.land[0], {stroke:"maroon", fill:"transparent"}); canvasDrawGraticule(context, projection, opts.land[0]); canvasClipSphere(context, projection); return context.canvas; }35:[] 30:{"id":"1deb0ab6010cb4df","slug":"analyse-comparative-projections","title":"Analyse comparative entre les distorsions des projections geoPylmyst, geoEquirectangular et geoMollweide","thumbnail":"15560fba568e95727d956c848e5040c2ef6b92da2386fdbea7e6227cca974b8d","access_level":"public","create_time":"$D2025-05-23T17:53:53.030Z","update_time":"$D2026-09-21T14:19:33.918Z","view_time":null,"first_public_time":"$D2025-05-28T06:17:11.633Z","has_unpublished_edits":null,"fork":{"id":"8941e2624ed51f6d","slug":"imago-projection-distorsion-analysis","title":"Imago Projection Distorsion Analysis","owner":{"id":"da2a32154638c457","login":"fil","name":"Fil"}},"stars":0,"starred":false,"owner":{"type":"team","id":"9784867a3e59436b","login":"linard-y","name":"","avatar_url":"https://avatars-next.observableusercontent.com/0ce44546efae24745b35d9327acbc99a3f3fdaeac3595375f92848f133b06ded","tier":"starter_2024"},"version":1874,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"c6e84137b8a39d94","login":"linard-y","name":"","avatar_url":"https://avatars-next.observableusercontent.com/0ce44546efae24745b35d9327acbc99a3f3fdaeac3595375f92848f133b06ded","tier":null}],"members":[{"type":"individual","id":"c6e84137b8a39d94","login":"linard-y","name":"","avatar_url":"https://avatars-next.observableusercontent.com/0ce44546efae24745b35d9327acbc99a3f3fdaeac3595375f92848f133b06ded","tier":null,"role":"editor"},{"type":"team","id":"9784867a3e59436b","login":"linard-y","name":"","avatar_url":"https://avatars-next.observableusercontent.com/0ce44546efae24745b35d9327acbc99a3f3fdaeac3595375f92848f133b06ded","tier":"starter_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"06f314aa212f58b3","slug":"mystara","title":"Mystara","owner":{"id":"9784867a3e59436b","login":"linard-y","name":""}},"type":"notebook","body":{"titling":"auto","title":"Analyse comparative entre les distorsions des projections geoPylmyst, geoEquirectangular et geoMollweide","cells":[{"id":0,"value":"# Analyse comparative entre les distorsions des projections geoPylmyst, geoEquirectangular et geoMollweide\n\n\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1197,"value":"## Distorsion surfacique","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":976,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":983,"value":"L'IDSG est le rapport entre les distorsions surfaciques minimale et maximale. L'indice parfait (pour les projections équivalente) est égal à 1.`\n \n **Indice de Distortion surfacique globale (IDSG) :** \ngeoPylmyst** ${IDSG.geoPylmyst.toFixed(2)} **geoEquirectangular** ${IDSG.geoEquirectangular.toFixed(2)} **geoMollweide** ${IDSG.geoMollweide.toFixed(2)}**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":992,"value":"L'IDSC est le rapport entre les dispsersions surfaciques minimale et maximale parmi les aires calculées à partir des points situés sur des masses continentales. L'indice parfait (pour les projections équivalente) est égal à 1.\n \n**Indice de Distortion surfacique continentale (IDSC) :** \ngeoPylmyst** ${IDSC.geoPylmyst.toFixed(2)} **geoEquirectangular** ${IDSC.geoEquirectangular.toFixed(2)} **geoMollweide** ${IDSC.geoMollweide.toFixed(2)} **","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1023,"value":"La différence entre l'IDSG et l'IDSC tient uniquement dans la répartition des masses continentales par rapport à la localisation des zones de distorsions plus ou moins fortes. Si les zones océanographiques n'ont pas beaucoup d'importance pour l'objectif final de la représentation cartographique alors mieux vaut considérer l'IDSC pour juger de la projection à utiliser. Dans le cas contraire où les masses continentales sont autant utiles que les zones océanographiques alors l'IDSG doit être privilégié.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":294,"value":"md`Les cartes ci-dessous permettent de localiser les variations de distorsion surfacique pour les projections geoPylmyst, geoEquirectangular et geoMollweide avec une même échelle de couleur. Le point rouge indique le point de référence.\n\n- blanc = distortion nulle (c'est-à-dire aire égale à celle du point de référence)\n- vert = aire < aire de refrerence\n- jaune or = aire > aire de refernce.\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1466,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1433,"value":"md`Les niveaux de distorion verts (inférieur à la référence) n'apparaissent pas dans ces cartes ce qui signifie que la référence choisie est l'un des points où la distorsion est la plus faible quelque soit le système de projection. Cette constatation est logique puisque la projection geoPylmyst est une projection gnomonique face centrée et que la référence est le centre d'une face par consequent il n'y a pas de déformation au centre des faces de l'icosaedre. De même, pour la projection geoEquirectangular, cette projection est cylindrique avec un ellipsoïde tangent au niveau de l'equateur et la référence est trés proche de l'equateur donc pas de déformation au niveau de l'equateur. La projection Mollweide est quant à elle une projection dite \"équivalente\" ce qui signifie qu'elle conserve les aires en tout point.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1199,"value":"## Distorsion angulaire (de forme)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1107,"value":"A chaque point P(${tex`\\lambda`}, ${tex`\\varphi`}) du globe, le triplet de points P(${tex`\\lambda`}, ${tex`\\varphi`}), P${tex`_1`}(${tex`\\lambda`} + ${tex`\\epsilon`}, ${tex`\\varphi`}]), P${tex`_2`}(${tex`\\lambda`}, ${tex`\\varphi`} + ${tex`\\epsilon`}/cos(${tex`\\varphi`})) forme un angle rectangle en P. Par comparaison avec ${tex`\\frac{\\pi}{2}`}, l'angle formé par les projetés de ces 3 points nous renseignent donc sur la distorsion angulaire au point P considéré. C'est la base du calcul de la distorsion angulaire. Les indicateurs IDAG et IDAC sont la valeur maximale du log de ces déformations angulaires parmi les valeurs à l'échelle du globe (IDAG) ou uniquement sur les masses continentales (IDAC). L'indice parfait, celui des projections conformes, est égal à 0.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1171,"value":"**IDAG:** geoPylmyst **${IDAG.geoPylmyst.toFixed(2)}** geoEquirectangular: **${IDAG.geoEquirectangular.toFixed(2)} **geoMollweide** ${IDAG.geoMollweide.toFixed(2)}**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":296,"value":"**IDAC:** geoPylmyst **${IDAC.geoPylmyst.toFixed(2)}** geoEquirectangular: **${IDAC.geoEquirectangular.toFixed(2)} **geoMollweide** ${IDAC.geoMollweide.toFixed(2)}**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":432,"value":"ANGULAR = {\n\n const map1 = mapfillContours(p => distorsion(p, projection1).angle, points, projection1, {\n width:2*dim1[0],\n height:2*dim1[1],\n margins:[6,6],\n land:[land],\n fill: colorAngle\n });\n \n\n const map2 = mapfillContours(p => distorsion(p, projection2).angle, points, projection2, {\n width:2*dim2[0],\n height:2*dim2[1],\n land:[land],\n fill: colorAngle\n });\n\n const map3 = mapfillContours(p => distorsion(p, projection3).angle, points, projection3, {\n width:2*dim3[0],\n height:2*dim3[1],\n land:[land],\n fill: colorAngle\n });\n \n return html`${map1}${map2}${map3}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1489,"value":"md`Contrairement aux projections geoEquirectangular et geoMollweide, on constate que la projection geoPylmyst est trés proche d'une projection conforme puisque les distortsion angulaire sont faibles partout sur la carte.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1202,"value":"## Indicatrices de Tissot","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":292,"value":"Pour apprécier les différences de déformation entre les trois projections, on peut également représenter les **Indicatrices de Tissot**. Inventé par le cartographe français Nicolas Auguste Tissot, cette méthode datant du XIXème siècle a pour principe la représentation de la projection d’une série de petits cercles tracés régulièrement sur la carte plane. On visualise leurs transformations induites par la projection. Cette méthode permet ainsi d’appréhender d’un seul coup d’œil les déformations, tant en matière de surface qu’en matière d’angle.\n\nLes modes de projection dits conformes préservent la forme circulaire des indicatrices, mais pas leur taille (ces projections conservent donc les formes des objets représentés, mais pas leur surface). Les modes de projection dits équivalents préservent la surface des indicatrices, mais pas leur forme, ce sont des ellipses (les formes sont altérées, mais pas les surfaces).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":676,"value":"TISSOT_MAPS = {\n\n const map1 = mapTissot(projection1, {\n width:2*dim1[0],\n height:2*dim1[1],\n margins:[6,6],\n land:[land]\n });\n\n const map2 = mapTissot(projection2, {\n width:2*dim2[0],\n height:2*dim2[1],\n land:[land]\n });\n\n\n const map3 = mapTissot(projection3, {\n width:2*dim3[0],\n height:2*dim3[1],\n land:[land]\n });\n\n\n return html`${map1}${map2}${map3}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1204,"value":"## Orientation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":508,"value":"**Orientation**\n\nLes cartes ci-dessous illustrent la la variation d'angle entre la direction Nord et l'axe reliant les pôles sur la carte projetée. Autrement dit, les inclinaisons des grands cercles de la carte par rapport à un axe vertical. Les variations d'orientation très marquées dans les cartes projetées sur des développements polyedriques rendent généralement ces cartes peu propice à être utilisées pour illustrer un trajet. De plus, ces variations expliquent le rendu, souvent en ligne brisée, de la ligne d’équateur.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1614,"value":"{\n\n const map1 = mapfillContours(p => distorsion(p, projection1).orientation, points, projection1, {\n width:2*dim1[0],\n height:2*dim1[1],\n margins:[6,6],\n land:[land],\n fill: colorOrientation\n });\n \n\n const map2 = mapfillContours(p => distorsion(p, projection2).orientation, points, projection2, {\n width:2*dim2[0],\n height:2*dim2[1],\n land:[land],\n fill: colorOrientation\n });\n\n const map3 = mapfillContours(p => distorsion(p, projection3).orientation, points, projection3, {\n width:2*dim3[0],\n height:2*dim3[1],\n land:[land],\n fill: colorOrientation\n });\n \n return html`${map1}${map2}${map3}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":328,"value":"N = 6000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1757,"value":"dim1 = [250,332]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":812,"value":"MoOmgaia = {\n\n const proj = geoPylmyst()\n .angle(210)\n .center([176.33671292158206, 44.80877202222518])\n .fitExtent([[6, 6], [dim1[0]*2+6,dim1[1]*2+6]], {type:\"Sphere\"})\n .precision(1e-5);\n \n return getPylmystFoldout(proj, {ε: 1e-3}); \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1380,"value":"projection1 = MoOmgaia.projection","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1808,"value":"dim2 = [166, 332]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":646,"value":"projection2 = d3.geoEquirectangular().angle(90).fitExtent([[6, 6], dim2.map(d => d*2+6)], {type:\"Sphere\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1813,"value":"dim3 = [426, 202]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1414,"value":"projection3 = d3.geoMollweide().fitExtent([[6, 6], dim3.map(d => d*2+6)], {type:\"Sphere\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1371,"value":"refPoint = [25.16326068168867, 8.903776840824202]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1589,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":358,"value":"points = {\n const phi = (1 + Math.sqrt(5)) / 2;\n return Array.from({ length: N }, (_, i) => {\n const [x, y] = [i / phi, (i + 0.5) / N];\n return [(x * 360) % 360, (Math.acos(2 * y - 1) / Math.PI) * 180 - 90];\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":145,"value":"inLand = points.map(d => d3.geoContains(land, d))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1019,"value":"IDSG = {\n const e = d3.extent(delta1, d => d.area);\n const e2 = d3.extent(delta2, d => d.area);\n const e3 = d3.extent(delta3, d => d.area);\n return({geoPylmyst: e[1] / e[0], geoEquirectangular:e2[1] / e2[0], geoMollweide:e3[1] / e3[0]});\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":184,"value":"IDSC = {\n const e = d3.extent(delta1.filter((_, i) => inLand[i]), d => d.area);\n const e2 = d3.extent(delta2.filter((_, i) => inLand[i]), d => d.area);\n const e3 = d3.extent(delta3.filter((_, i) => inLand[i]), d => d.area);\n return({geoPylmyst: e[1] / e[0], geoEquirectangular:e2[1] / e2[0], geoMollweide:e3[1] / e3[0]});\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1164,"value":"IDAG = ({\n geoPylmyst: d3.max(delta1, d => d.angle),\n geoEquirectangular: d3.max(delta2, d => d.angle),\n geoMollweide: d3.max(delta3, d => d.angle)\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1161,"value":"IDAC = ({\n geoPylmyst: d3.max(delta1.filter((_, i) => inLand[i]), d => d.angle),\n geoEquirectangular: d3.max(delta2.filter((_, i) => inLand[i]), d => d.angle),\n geoMollweide: d3.max(delta3.filter((_, i) => inLand[i]), d => d.angle)\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":97,"value":"function distorsion(point, projection) {\n const [c, n, e] = [\n point,\n [point[0], point[1] + epsilon],\n [point[0] + epsilon / Math.cos(point[1] * radians), point[1]]\n ].map(projection);\n\n const vn = { x: n[0] - c[0], y: n[1] - c[1] };\n const ve = { x: e[0] - c[0], y: e[1] - c[1] };\n\n // surface d'un quadrilaère\n const area = Math.log((ve.y * vn.x - ve.x * vn.y) / epsilon ** 2);\n \n const s1ps2 = Math.hypot(ve.x + vn.y, ve.y - vn.x);\n \n const s1ms2 = Math.hypot(ve.x - vn.y, ve.y + vn.x);\n \n const angle = (s1ps2 - s1ms2) / (s1ps2 + s1ms2);\n \n const orientation = Math.atan2(n[1] - c[1], n[0] - c[0]);\n\n return {\n area,\n angle: abs(log(abs(angle))),\n orientation: orientation==Math.PI?0:orientation/Math.PI\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"delta1 = points.map(d => distorsion(d, projection1))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":658,"value":"delta2 = points.map(d => distorsion(d, projection2))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1437,"value":"delta3 = points.map(d => distorsion(d, projection3))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1583,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":136,"value":"ref = (proj) => distorsion(refPoint , proj).area","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":741,"value":"function rearrange(coordinates) {\n coordinates.flat().forEach(d => d.reverse());\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1516,"value":"getContours = (valuePoint, points, options={}) => {\n let opts = Object.assign({\n thresholds: 100,\n }, options);\n\n const v = d3.geoVoronoi(points);\n \n return d3\n .tricontour()\n .thresholds(opts.thresholds)\n .triangulate(() => v.delaunay.delaunay)\n .pointInterpolate((i, j, a) => d3.geoInterpolate(points[i], points[j])(a))\n .value(valuePoint)\n .ringsort((rings) => [rings]);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":431,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1586,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":77,"value":"tissot = {\n const circle = d3.geoCircle().radius(4.5),\n tissot = {\n type: \"MultiPolygon\",\n coordinates: []\n };\n\n [-60, -30, 0, 30, 60].forEach(lat => {\n [-150, -120, -90, -60, -30, 0, 30, 60, 90, 120, 150, 180].forEach(lon => {\n tissot.coordinates.push([lon, lat]);\n });\n });\n tissot.coordinates.push([0, 90]);\n tissot.coordinates.push([0, -90]);\n tissot.coordinates = tissot.coordinates.map(\n d => circle.center(d)().coordinates\n );\n\n return tissot;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"function mapTissot(projection, options) {\n\n let opts = Object.assign({\n width:960,\n height:480,\n land:[],\n margins:[6,6],\n }, options);\n\n const extent = ({width:opts.width+2*opts.margins[0], height:opts.height+2*opts.margins[1]});\n\n const context = DOM.context2d(extent.width, extent.height);\n var path = d3.geoPath(projection, context);\n\n canvasSetBackground(context, extent.width, extent.height, {fill:\"#000\"});\n\n context.translate(opts.margins[0], opts.margins[1]);\n\n canvasClipSphere(context, projection);\n canvasDrawSphere(context, projection, {fill: \"#fff\"});\n canvasDrawLand(context, projection, opts.land[0], {stroke:\"maroon\", fill:\"transparent\"});\n canvasDrawGraticule(context, projection, opts.land[0]);\n \n context.beginPath(),\n path(tissot),\n context.fillStyle = \"rgba(255,99,71,.5)\",\n context.fill();\n \n canvasDrawSphere(context, projection);\n canvasClipSphere(context, projection);\n \n\n return context.canvas;\n \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1600,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":554,"value":"colorArea = d3\n .scaleLinear()\n .range([\"green\", \"white\", \"gold\"])\n .domain([-0.8, 0, 0.8])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":212,"value":"colorAngle = d3\n .scaleLinear()\n .domain([0, 1])\n .range([\"white\", \"gold\"])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":954,"value":"colorOrientation = d3\n .scaleLinear()\n .domain([-1, -0.5, 0, 0.5, 1])\n .range([\"green\", \"white\", \"gold\", \"white\", \"green\"])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1637,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":131,"value":"d3 = require(\"d3@5\", \"d3-geo-projection@2\", \"d3-geo-voronoi@1\", \"https://recifs.neocities.org/imago-dev/d3-geo-polygon.js?\" +\n Math.random(), \"d3-delaunay\", \"d3-hsv\", \"d3-tricontour@1\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":98,"value":"import {abs, cos, epsilon, log, radians} from \"@fil/math\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":672,"value":"import {world as land, geoPylmyst, getPylmystFoldout, canvasDrawSphere, canvasDrawLand, canvasDrawGraticule, canvasSetBackground, canvasClipSphere} from \"@linard-y/geopylmyst\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1"}} 31:"$30:body"