{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The interpolant is constructed by triangulating the input data with Qhull " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": ", and constructing a piecewise cubic interpolating Bezier polynomial on each triangle, using a Clough-Tocher scheme " }, { "__type": "CitationReference", "__tag": 4063, "label": "CT" }, { "__type": "Text", "__tag": 4046, "value": ". The interpolant is guaranteed to be continuously differentiable." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The gradients of the interpolant are chosen so that the curvature of the interpolating surface is approximatively minimized. 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0.5\ny = rng.random(10) - 0.5\nz = np.hypot(x, y)\nX = np.linspace(min(x), max(x))\nY = np.linspace(min(y), max(y))\nX, Y = np.meshgrid(X, Y) # 2D grid for interpolation\ninterp = CloughTocher2DInterpolator(list(zip(x, y)), z)\nZ = interp(X, Y)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.pcolormesh(X, Y, Z, shading='auto')\nplt.plot(x, y, \"ok\", label=\"input point\")\nplt.legend(loc=\"upper right\")\nplt.colorbar()\nplt.axis(\"equal\")\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-c2857834541c0125.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "LinearNDInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._interpnd:LinearNDInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Piecewise linear interpolator in N > 1 dimensions." } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "NearestNDInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._ndgriddata:NearestNDInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Nearest-neighbor interpolator in N > 1 dimensions." } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "RegularGridInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._rgi:RegularGridInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Interpolator on a regular or rectilinear grid in arbitrary dimensions (" }, { "__type": "InlineRole", "__tag": 4003, "value": "interpn", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " wraps this class)." } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "griddata", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._ndgriddata:griddata" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Interpolate unstructured D-D data." } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "interpn", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._rgi:interpn" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Interpolation on a regular grid or rectilinear grid." } ] } ], "type": null } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "points", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "values", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "fill_value", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "nan" }, { "__type": "SigParam", "__tag": 4030, "name": "tol", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1e-06" }, { "__type": "SigParam", "__tag": 4030, "name": "maxiter", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "400" }, { "__type": "SigParam", "__tag": 4030, "name": "rescale", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "CloughTocher2DInterpolator" }, "references": [ ".. [1] http://www.qhull.org/", "", ".. [CT] See, for example,", " P. Alfeld,", " ''A trivariate Clough-Tocher scheme for tetrahedral data''.", " Computer Aided Geometric Design, 1, 169 (1984);", " G. Farin,", " ''Triangular Bernstein-Bezier patches''.", " Computer Aided Geometric Design, 3, 83 (1986).", "", ".. [Nielson83] G. Nielson,", " ''A method for interpolating scattered data based upon a minimum norm", " network''.", " Math. Comp., 40, 253 (1983).", "", ".. [Renka84] R. J. Renka and A. K. Cline.", " ''A Triangle-based C1 interpolation method.'',", " Rocky Mountain J. Math., 14, 223 (1984)." ], "qa": "scipy.interpolate._interpnd:CloughTocher2DInterpolator", "arbitrary": [], "local_refs": [ "__call__", "fill_value", "maxiter", "points", "rescale", "tol", "values" ] }