Contour plot (#1540)

* ContourPlot is implemented, supporting the Contours option and
supporting two kinds of contour plot (see image).
* In the case of Automatic PlotRanges, ContourPlot and others now pass
through to Graphics a PlotRange reflecting the specified {x,xmin,xmax}
etc. ranges, which may be different from the ranges of x, etc. found in
the emitted graphics data, so that the correct range can be plotted.
This allows e.g. contour plots that may have only contours with x,y
values for a subset of the specified range to be correctly plotted.
* The above tickled a bug in boxing so this was worked around.
* ContourPlot requires skimage but the existing message about missing
modules wasn't showing the module name, so this was fixed.
<img width="60%" alt="image"
src="https://github.com/user-attachments/assets/7b2212a8-8bce-40b2-b454-45069618daf2"
/>

Author: bdlucas1

SYMBOLS_MANIFEST.txt

@@ -265,6 +265,7 @@ System`Context
 System`Contexts
 System`Continue
 System`ContinuedFraction
+System`ContourPlot
 System`Convert`B64Dump`B64Decode
 System`Convert`B64Dump`B64Encode
 System`ConvertersDump`$ExtensionMappings

mathics/builtin/box/graphics3d.py

@@ -250,6 +250,17 @@ def _prepare_elements(self, elements, options, max_width=None):
             self.background_color = elements.background_color
 
         def calc_dimensions(final_pass=True):
+            # TODO: the code below is broken in any other case but Automatic
+            # because it calls elements.translate which is not implemented.
+            # Plots may pass specific plot ranges, triggering this deficiency
+            # and causing tests to fail The following line avoids this,
+            # and it should not change the behavior of any case which did
+            # previously fail with an exception.
+            #
+            # This code should be DRYed (together with the very similar code
+            # for the 2d case), and the missing .translate method added.
+            plot_range = ["System`Automatic"] * 3
+
             if "System`Automatic" in plot_range:
                 xmin, xmax, ymin, ymax, zmin, zmax = elements.extent()
             else:
@@ -291,7 +302,7 @@ def calc_dimensions(final_pass=True):
                     elif zmin == zmax:
                         zmin -= 1
                         zmax += 1
-                elif isinstance(plot_range[1], list) and len(plot_range[1]) == 2:
+                elif isinstance(plot_range[1], list) and len(plot_range[2]) == 2:
                     zmin, zmax = list(map(float, plot_range[2]))
                     zmin = elements.translate((0, 0, zmin))[2]
                     zmax = elements.translate((0, 0, zmax))[2]

mathics/builtin/drawing/plot.py

@@ -37,6 +37,7 @@
     SymbolLine,
     SymbolLog10,
     SymbolNone,
+    SymbolPlotRange,
     SymbolRGBColor,
     SymbolSequence,
     SymbolStyle,
@@ -67,13 +68,15 @@
     from mathics.eval.drawing.plot3d_vectorized import (
         eval_ComplexPlot,
         eval_ComplexPlot3D,
+        eval_ContourPlot,
         eval_DensityPlot,
         eval_Plot3D,
     )
 else:
     from mathics.eval.drawing.plot3d import (
         eval_ComplexPlot,
         eval_ComplexPlot3D,
+        eval_ContourPlot,
         eval_DensityPlot,
         eval_Plot3D,
     )
@@ -467,7 +470,7 @@ def error(self, what, *args, **kwargs):
     def __init__(self, expr, range_exprs, options, evaluation):
         self.evaluation = evaluation
 
-        # plot ranges
+        # plot ranges of the form {x,xmin,xmax} etc.
         self.ranges = []
         for range_expr in range_exprs:
             if not range_expr.has_form("List", 3):
@@ -488,6 +491,19 @@ def __init__(self, expr, range_exprs, options, evaluation):
                 self.error(expr, "invrange", range_expr)
             self.ranges.append(range)
 
+        # Contours option
+        contours = expr.get_option(options, "Contours", evaluation)
+        if contours is not None:
+            c = contours.to_python()
+            if not (
+                c == "System`Automatic"
+                or isinstance(c, int)
+                or isinstance(c, tuple)
+                and all(isinstance(cc, (int, float)) for cc in c)
+            ):
+                self.error(expr, "invcontour", contours)
+            self.contours = c
+
         # Mesh option
         mesh = expr.get_option(options, "Mesh", evaluation)
         if mesh not in (SymbolNone, SymbolFull, SymbolAll):
@@ -579,6 +595,9 @@ class _Plot3D(Builtin):
             "Plot range `1` must be of the form {variable, min, max}, "
             "where max > min."
         ),
+        "invcontour": (
+            "Contours option must be Automatic, an integer, or a list of numbers."
+        ),
     }
 
     # Plot3D, ComplexPlot3D
@@ -633,6 +652,39 @@ def eval(
         graphics = self.eval_function(plot_options, evaluation)
         if not graphics:
             return
+
+        # Expand PlotRange option using the {x,xmin,xmax} etc. range specifications
+        # Pythonize it, so Symbol becomes str, numeric becomes int or float
+        plot_range = self.get_option(options, str(SymbolPlotRange), evaluation)
+        plot_range = plot_range.to_python()
+        dim = 3 if self.graphics_class is Graphics3D else 2
+        if isinstance(plot_range, str):
+            # PlotRange -> Automatic becomes PlotRange -> {Automatic, ...}
+            plot_range = [str(SymbolAutomatic)] * dim
+        if isinstance(plot_range, (int, float)):
+            # PlotRange -> s becomes PlotRange -> {Automatic,...,{-s,s}}
+            pr = plot_range
+            plot_range = [str(SymbolAutomatic)] * dim
+            plot_range[-1] = [-pr, pr]
+        elif isinstance(plot_range, (list, tuple)) and isinstance(
+            plot_range[0], (int, float)
+        ):
+            # PlotRange -> {s0,s1} becomes  PlotRange -> {Automatic,...,{s0,s1}}
+            pr = plot_range
+            plot_range = [str(SymbolAutomatic)] * dim
+            plot_range[-1] = pr
+
+        # now we have a list of length dim
+        # handle Automatic ~ {xmin,xmax} etc.
+        for i, (pr, r) in enumerate(zip(plot_range, plot_options.ranges)):
+            # TODO: this treats Automatic and Full as the same, which isn't quite right
+            if isinstance(pr, str) and not isinstance(r[1], complex):
+                plot_range[i] = r[1:]  # extract {xmin,xmax} from {x,xmin,xmax}
+
+        # unpythonize and update PlotRange option
+        options[str(SymbolPlotRange)] = to_mathics_list(*plot_range)
+
+        # generate the Graphics[3D] result
         graphics_expr = graphics.generate(
             options_to_rules(options, self.graphics_class.options)
         )
@@ -809,6 +861,32 @@ class ComplexPlot(_Plot3D):
     graphics_class = Graphics
 
 
+class ContourPlot(_Plot3D):
+    """
+    <url>:WMA link: https://reference.wolfram.com/language/ref/ContourPlot.html</url>
+    <dl>
+      <dt>'Contour'[$f$, {$x$, $x_{min}$, $x_{max}$}, {$y$, $y_{min}$, $y_{max}$}]
+      <dd>creates a two-dimensional contour plot ofh $f$ over the region
+          $x$ ranging from $x_{min}$ to $x_{max}$ and $y$ ranging from $y_{min}$ to $y_{max}$.
+
+          See <url>:Drawing Option and Option Values:
+    /doc/reference-of-built-in-symbols/graphics-and-drawing/drawing-options-and-option-values
+    </url> for a list of Plot options.
+    </dl>
+
+    """
+
+    requires = ["skimage"]
+    summary_text = "creates a contour plot"
+    expected_args = 3
+    options = _Plot3D.options2d | {"Contours": "Automatic"}
+    # TODO: other options?
+
+    many_functions = True
+    eval_function = staticmethod(eval_ContourPlot)
+    graphics_class = Graphics
+
+
 class DensityPlot(_Plot3D):
     """
     <url>:WMA link: https://reference.wolfram.com/language/ref/DensityPlot.html</url>

mathics/core/builtin.py

@@ -852,12 +852,14 @@ class UnavailableFunction:
 
     def __init__(self, builtin):
         self.name = builtin.get_name()
+        self.requires = builtin.requires
 
     def __call__(self, **kwargs):
         kwargs["evaluation"].message(
             "General",
             "pyimport",  # see messages.py for error message definition
             strip_context(self.name),
+            ", ".join(self.requires),
         )
 
 

mathics/core/systemsymbols.py

@@ -228,6 +228,7 @@
 SymbolPiecewise = Symbol("System`Piecewise")
 SymbolPlot = Symbol("System`Plot")
 SymbolPlotLabel = Symbol("System`PlotLabel")
+SymbolPlotRange = Symbol("System`PlotRange")
 SymbolPlotRangeClipping = Symbol("System`PlotRangeClipping")
 SymbolPlotRegion = Symbol("System`PlotRegion")
 SymbolPlus = Symbol("System`Plus")

mathics/eval/drawing/plot3d.py

@@ -506,3 +506,10 @@ def eval_ComplexPlot(
     evaluation: Evaluation,
 ):
     return None
+
+
+def eval_ContourPlot(
+    plot_options,
+    evaluation: Evaluation,
+):
+    return None