Graphics overhault

mathics/builtin/graphics3d.py

@@ -114,21 +114,20 @@ class Graphics3D(Graphics):
      . import three;
      . import solids;
      . size(6.6667cm, 6.6667cm);
-     . currentprojection=perspective(2.6,-4.8,4.0);
+     . currentprojection=perspective(1.3,-2.4,2.0);
      . currentlight=light(rgb(0.5,0.5,1), specular=red, (2,0,2), (2,2,2), (0,2,2));
-     . path3 g=(0,1,0)--(0.20791,0.97815,0)--(0.40674,0.91355,0)--(0.58779,0.80902,0)--(0.74314,0.66913,0)--(0.86603,0.5,0)--(0.95106,0.30902,0)--(0.99452,0.10453,0)--(0.99452,-0.10453,0)--(0.95106,-0.30902,0)--(0.86603,-0.5,0)--(0.74314,-0.66913,0)--(0.58779,-0.80902,0)--(0.40674,-0.91355,0)--(0.20791,-0.97815,0)--(5.6655e-16,-1,0)--(-0.20791,-0.97815,0)--(-0.40674,-0.91355,0)--(-0.58779,-0.80902,0)--(-0.74314,-0.66913,0)--(-0.86603,-0.5,0)--(-0.95106,-0.30902,0)--(-0.99452,-0.10453,0)--(-0.99452,0.10453,0)--(-0.95106,0.30902,0)--(-0.86603,0.5,0)--(-0.74314,0.66913,0)--(-0.58779,0.80902,0)--(-0.40674,0.91355,0)--(-0.20791,0.97815,0)--(1.5314e-15,1,0)--cycle;dot(g, rgb(0, 0, 0));
-     . draw(((-0.99452,-1,-1)--(0.99452,-1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((-0.99452,1,-1)--(0.99452,1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((-0.99452,-1,1)--(0.99452,-1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((-0.99452,1,1)--(0.99452,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((-0.99452,-1,-1)--(-0.99452,1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((0.99452,-1,-1)--(0.99452,1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((-0.99452,-1,1)--(-0.99452,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((0.99452,-1,1)--(0.99452,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((-0.99452,-1,-1)--(-0.99452,-1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((0.99452,-1,-1)--(0.99452,-1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((-0.99452,1,-1)--(-0.99452,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
-     . draw(((0.99452,1,-1)--(0.99452,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,0,0)--(1,0,0)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,1,0)--(1,1,0)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,0,1)--(1,0,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,1,1)--(1,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,0,0)--(0,1,0)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((1,0,0)--(1,1,0)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,0,1)--(0,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((1,0,1)--(1,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,0,0)--(0,0,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((1,0,0)--(1,0,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((0,1,0)--(0,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
+     . draw(((1,1,0)--(1,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1));
      . \end{asy}
     """
 
@@ -763,8 +762,6 @@ def total_extent_3d(extents):
 
 
 class Graphics3DElements(_GraphicsElements):
-    coords = Coords3D
-
     def __init__(self, content, evaluation, neg_y=False):
         super(Graphics3DElements, self).__init__(content, evaluation)
         self.neg_y = neg_y
@@ -774,6 +771,10 @@ def __init__(self, content, evaluation, neg_y=False):
             self.pixel_width
         ) = self.pixel_height = self.extent_width = self.extent_height = None
 
+    def make_coords(self, points):
+        print("make_coords3d",points)
+        return [Coords3D(self, p) for p in points]
+
     def extent(self, completely_visible_only=False):
         return total_extent_3d([element.extent() for element in self.elements])
 
@@ -799,6 +800,7 @@ def get_style_class(self):
 
 class Point3DBox(PointBox):
     def init(self, *args, **kwargs):
+        print("Point3DBox.init")
         super(Point3DBox, self).init(*args, **kwargs)
 
     def process_option(self, name, value):
@@ -902,6 +904,7 @@ def _apply_boxscaling(self, boxscale):
 class Polygon3DBox(PolygonBox):
     def init(self, *args, **kwargs):
         self.vertex_normals = None
+        self.vertex_colors = None
         super(Polygon3DBox, self).init(*args, **kwargs)
 
     def process_option(self, name, value):

mathics/builtin/image.py

@@ -20,6 +20,7 @@
     convert as convert_color,
     colorspaces as known_colorspaces,
 )
+#from mathics.layout.client import WebEngineError
 
 import base64
 import functools
@@ -2569,4 +2570,43 @@ def color_func(
         wc.generate_from_frequencies(freq)
 
         image = wc.to_image()
-        return Image(numpy.array(image), "RGB")
+        return Image(numpy.array(image), 'RGB')
+
+
+class Rasterize(Builtin):
+    requires = _image_requires
+
+    options = {
+        'RasterSize': '300',
+    }
+
+    def apply(self, expr, evaluation, options):
+        'Rasterize[expr_, OptionsPattern[%(name)s]]'
+
+        raster_size = self.get_option(options, 'RasterSize', evaluation)
+        if isinstance(raster_size, Integer):
+            s = raster_size.get_int_value()
+            py_raster_size = (s, s)
+        elif raster_size.has_form('List', 2) and all(isinstance(s, Integer) for s in raster_size.leaves):
+            py_raster_size = tuple(s.get_int_value for s in raster_size.leaves)
+        else:
+            return
+
+        mathml = evaluation.format_output(expr, 'xml')
+        try:
+            svg = evaluation.output.mathml_to_svg(mathml)
+            png = evaluation.output.rasterize(svg, py_raster_size)
+
+            stream = BytesIO()
+            stream.write(png)
+            stream.seek(0)
+            im = PIL.Image.open(stream)
+            # note that we need to get these pixels as long as stream is still open,
+            # otherwise PIL will generate an IO error.
+            pixels = numpy.array(im)
+            stream.close()
+
+            return Image(pixels, 'RGB')
+        except WebEngineError as e:
+            evaluation.message(
+                'General', 'nowebeng', 'Rasterize[] did not succeed: ' + str(e), once=True)

mathics/builtin/inout.py

@@ -1878,6 +1878,7 @@ class General(Builtin):
         'notboxes': "`1` is not a valid box structure.",
 
         'pyimport': "`1`[] is not available. Your Python installation misses the \"`2`\" module.",
+        'nowebeng': "Web Engine is not available: `1`",
     }
 
 

mathics/builtin/plot.py

@@ -818,6 +818,14 @@ def find_excl(excl):
                 meshpoints = [Expression("List", xx, yy) for xx, yy in points]
                 graphics.append(Expression("Point", Expression("List", *meshpoints)))
 
+        # we need the PrecomputeTransformations option here. to understand why, try Plot[1+x*0.000001, {x, 0, 1}]
+        # without it. in Graphics[], we set up a transformation that scales a very tiny area to a very large area.
+        # unfortunately, most browsers seem to have problems with scaling stroke width properly. since we scale a
+        # very tiny area, we specify a very small stroke width (e.g. 1e-6) which is then scaled. but most browsers
+        # simply round this stroke width to 0 before scaling, so we end up with an empty plot. in order to fix this,
+        # Transformation -> Precomputed simply gets rid of the SVG transformations and passes the scaled coordinates
+        # into the SVG. this also has the advantage that we can precompute with arbitrary precision using mpmath.
+        options['System`Transformation'] = String('Precomputed')                
         return Expression(
             "Graphics", Expression("List", *graphics), *options_to_rules(options)
         )
@@ -1243,6 +1251,11 @@ def labels(names):
         )
 
 
+
+
+
+
+
 class Histogram(Builtin):
     """
     <dl>

mathics/builtin/tensors.py

@@ -482,3 +482,100 @@ def is_boolean(x):
             return 'ColorDistance'
 
         return None
+
+
+
+class TransformationFunction(Builtin):
+    """
+    <dl>
+    <dt>'TransformationFunction[$m$]'
+        <dd>represents a transformation.
+    </dl>
+
+    >> RotationTransform[Pi].TranslationTransform[{1, -1}]
+     = TransformationFunction[{{-1, 0, -1}, {0, -1, 1}, {0, 0, 1}}]
+
+    >> TranslationTransform[{1, -1}].RotationTransform[Pi]
+     = TransformationFunction[{{-1, 0, 1}, {0, -1, -1}, {0, 0, 1}}]
+    """
+
+    rules = {
+        'Dot[TransformationFunction[a_], TransformationFunction[b_]]': 'TransformationFunction[a . b]',
+        'TransformationFunction[m_][v_]': 'Take[m . Join[v, {1}], Length[v]]',
+    }
+
+
+class TranslationTransform(Builtin):
+    """
+    <dl>
+    <dt>'TranslationTransform[$v$]'
+        <dd>gives the translation by the vector $v$.
+    </dl>
+
+    >> TranslationTransform[{1, 2}]
+     = TransformationFunction[{{1, 0, 1}, {0, 1, 2}, {0, 0, 1}}]
+    """
+
+    rules = {
+        'TranslationTransform[v_]':
+            'TransformationFunction[IdentityMatrix[Length[v] + 1] + '
+            '(Join[ConstantArray[0, Length[v]], {#}]& /@ Join[v, {0}])]',
+    }
+
+
+class RotationTransform(Builtin):
+    """
+    <dl>
+    <dt>'RotationTransform[$phi$]'
+        <dd>gives a rotation by $phi$.
+    <dt>'RotationTransform[$phi$, $p$]'
+        <dd>gives a rotation by $phi$ around the point $p$.
+    </dl>
+    """
+
+    rules = {
+        'RotationTransform[phi_]':
+            'TransformationFunction[{{Cos[phi], -Sin[phi], 0}, {Sin[phi], Cos[phi], 0}, {0, 0, 1}}]',
+        'RotationTransform[phi_, p_]':
+            'TranslationTransform[p] . RotationTransform[phi] . TranslationTransform[-p]',
+    }
+
+
+class ScalingTransform(Builtin):
+    """
+    <dl>
+    <dt>'ScalingTransform[$v$]'
+        <dd>gives a scaling transform of $v$. $v$ may be a scalar or a vector.
+    <dt>'ScalingTransform[$phi$, $p$]'
+        <dd>gives a scaling transform of $v$ that is centered at the point $p$.
+    </dl>
+    """
+
+    rules = {
+        'ScalingTransform[v_]':
+            'TransformationFunction[DiagonalMatrix[Join[v, {1}]]]',
+        'ScalingTransform[v_, p_]':
+            'TranslationTransform[p] . ScalingTransform[v] . TranslationTransform[-p]',
+    }
+
+
+class ShearingTransform(Builtin):
+    """
+    <dl>
+    <dt>'ShearingTransform[$phi$, {1, 0}, {0, 1}]'
+        <dd>gives a horizontal shear by the angle $phi$.
+    <dt>'ShearingTransform[$phi$, {0, 1}, {1, 0}]'
+        <dd>gives a vertical shear by the angle $phi$.
+    <dt>'ShearingTransform[$phi$, $u$, $u$, $p$]'
+        <dd>gives a shear centered at the point $p$.
+    </dl>
+    """
+
+    rules = {
+        'ShearingTransform[phi_, {1, 0}, {0, 1}]':
+            'TransformationFunction[{{1, Tan[phi], 0}, {0, 1, 0}, {0, 0, 1}}]',
+        'ShearingTransform[phi_, {0, 1}, {1, 0}]':
+            'TransformationFunction[{{1, 0, 0}, {Tan[phi], 1, 0}, {0, 0, 1}}]',
+        'ShearingTransform[phi_, u_, v_, p_]':
+            'TranslationTransform[p] . ShearingTransform[phi, u, v] . TranslationTransform[-p]',
+    }

mathics/core/evaluation.py

@@ -13,8 +13,11 @@
 from mathics_scanner import TranslateError
 
 from mathics import settings
+
+from mathics.layout.client import NoWebEngine
 from mathics.core.expression import ensure_context, KeyComparable, SymbolAborted
 
+
 FORMATS = [
     "StandardForm",
     "FullForm",
@@ -213,6 +216,9 @@ def get_data(self):
 
 
 class Output(object):
+    def __init__(self, web_engine=NoWebEngine()):
+        self.web_engine = web_engine
+
     def max_stored_size(self, settings) -> int:
         return settings.MAX_STORED_SIZE
 
@@ -225,6 +231,18 @@ def clear(self, wait):
     def display(self, data, metadata):
         raise NotImplementedError
 
+    def warn_about_web_engine(self):
+        return False
+
+    def assume_web_engine(self):
+        return self.web_engine.assume_is_available()
+
+    def mathml_to_svg(self, mathml):
+        return self.web_engine.mathml_to_svg(mathml)
+
+    def rasterize(self, svg, *args, **kwargs):
+        return self.web_engine.rasterize(svg, *args, **kwargs)
+
 
 class Evaluation(object):
     def __init__(
@@ -249,6 +267,7 @@ def __init__(
         self.quiet_all = False
         self.format = format
         self.catch_interrupt = catch_interrupt
+        self.once_messages = set()
 
         self.SymbolNull = Symbol("Null")
 
@@ -474,7 +493,7 @@ def get_quiet_messages(self):
             return []
         return value.leaves
 
-    def message(self, symbol, tag, *args) -> None:
+    def message(self, symbol, tag, *args, **kwargs) -> None:
         from mathics.core.expression import String, Symbol, Expression, from_python
 
         # Allow evaluation.message('MyBuiltin', ...) (assume
@@ -484,6 +503,11 @@ def message(self, symbol, tag, *args) -> None:
 
         pattern = Expression("MessageName", Symbol(symbol), String(tag))
 
+        if kwargs.get('once', False):
+            if pattern in self.once_messages:
+                return
+            self.once_messages.add(pattern)
+
         if pattern in quiet_messages or self.quiet_all:
             return
 

mathics/layout/__init__.py

@@ -0,0 +1,2 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-