improv: add support for custom modifiers

example/lib/pages/polygon_custom.dart

@@ -1,3 +1,5 @@
+import 'dart:math';
+
 import 'package:flutter/material.dart';
 import 'package:graphic/graphic.dart';
 
@@ -637,6 +639,54 @@ class PolygonCustomPage extends StatelessWidget {
                   ],
                 ),
               ),
+              Container(
+                child: const Text(
+                  'Custom Modifier',
+                  style: TextStyle(fontSize: 20),
+                ),
+                padding: const EdgeInsets.fromLTRB(20, 40, 20, 5),
+              ),
+              Container(
+                child: const Text(
+                  '- With dodge and size modifier that scales the interval element width to fit within its band',
+                ),
+                padding: const EdgeInsets.fromLTRB(10, 5, 10, 0),
+                alignment: Alignment.centerLeft,
+              ),
+              Container(
+                margin: const EdgeInsets.only(top: 10),
+                width: 350,
+                height: 300,
+                child: Chart(
+                  padding: (_) => const EdgeInsets.fromLTRB(40, 5, 10, 40),
+                  data: adjustData,
+                  variables: {
+                    'index': Variable(
+                      accessor: (Map map) => map['index'].toString(),
+                    ),
+                    'type': Variable(
+                      accessor: (Map map) => map['type'] as String,
+                    ),
+                    'value': Variable(
+                      accessor: (Map map) => map['value'] as num,
+                    ),
+                  },
+                  elements: [
+                    IntervalElement(
+                      position:
+                          Varset('index') * Varset('value') / Varset('type'),
+                      color: ColorAttr(
+                          variable: 'type', values: Defaults.colors10),
+                      size: SizeAttr(value: 2),
+                      modifiers: [DodgeSizeModifier()],
+                    )
+                  ],
+                  axes: [
+                    Defaults.horizontalAxis..tickLine = TickLine(),
+                    Defaults.verticalAxis,
+                  ],
+                ),
+              ),
               Container(
                 child: const Text(
                   'Candlestick Chart',
@@ -733,3 +783,90 @@ class PolygonCustomPage extends StatelessWidget {
     );
   }
 }
+
+/// Changes the position of elements while also updating their width to match
+/// the number of elements in a single band. Useful for bar charts when the
+/// width of the bars can be dynamic.
+@immutable
+class DodgeSizeModifier extends Modifier {
+  @override
+  bool operator ==(Object other) => other is DodgeSizeModifier;
+
+  @override
+  DodgeSizeGeomModifierOp toGeomModifierOp(ToGeomModifierOpParams params) {
+    return DodgeSizeGeomModifierOp(<String, dynamic>{
+      'form': params.form,
+      'scales': params.scales,
+      'groups': params.groups,
+      'coord': params.coord,
+    });
+  }
+}
+
+const _kBaseGroupPaddingHorizontal = 32.0;
+const _kXAxis = 1;
+const _kMinBarSize = 4.0;
+
+/// The dodge geometry modifier.
+class DodgeSizeGeomModifier extends GeomModifier {
+  DodgeSizeGeomModifier(this.band, this.coord);
+
+  final CoordConv coord;
+
+  /// The band ratio of each value. It represents the width of the interval the
+  /// [Aes]es have to position themselves within.
+  /// Its range is ]0, 1].
+  final double band;
+
+  @override
+  void modify(AesGroups value) {
+    final ratio = 1 / value.length;
+    final numGroups = value.length;
+    final groupHorizontalPadding = _kBaseGroupPaddingHorizontal / numGroups;
+    final invertedGroupPaddingHorizontal =
+        coord.invertDistance(groupHorizontalPadding, _kXAxis);
+
+    final effectiveBand = band - 2 * invertedGroupPaddingHorizontal;
+
+    final maxWidth = coord.convert(const Offset(1, 0)).dx;
+    final maxWidthInBand = effectiveBand * maxWidth;
+    final maxWidthPerAes = maxWidthInBand / numGroups;
+    final barHorizontalPadding = groupHorizontalPadding / 2;
+    final size = max(maxWidthPerAes - barHorizontalPadding, _kMinBarSize);
+
+    final bias = ratio * effectiveBand;
+
+    // Negatively shift half of the total bias.
+    var accumulated = -bias * (numGroups + 1) / 2;
+
+    for (final group in value) {
+      for (final aes in group) {
+        final oldPosition = aes.position;
+        aes.position = oldPosition
+            .map(
+              (point) => Offset(point.dx + accumulated + bias, point.dy),
+            )
+            .toList();
+
+        aes.size = size;
+      }
+      accumulated += bias;
+    }
+  }
+}
+
+class DodgeSizeGeomModifierOp extends GeomModifierOp<DodgeSizeGeomModifier> {
+  DodgeSizeGeomModifierOp(Map<String, dynamic> params) : super(params);
+
+  @override
+  DodgeSizeGeomModifier evaluate() {
+    final form = params['form'] as AlgForm;
+    final scales = params['scales'] as Map<String, ScaleConv>;
+    final coord = params['coord'] as CoordConv;
+
+    final xField = form.first[0];
+    final band = (scales[xField]! as DiscreteScaleConv).band;
+
+    return DodgeSizeGeomModifier(band, coord);
+  }
+}

lib/graphic.dart

@@ -125,12 +125,12 @@ export 'src/variable/transform/map.dart' show MapTrans;
 export 'src/variable/transform/proportion.dart' show Proportion;
 export 'src/variable/transform/sort.dart' show Sort;
 
-export 'src/scale/scale.dart' show Scale;
-export 'src/scale/discrete.dart' show DiscreteScale;
-export 'src/scale/continuous.dart' show ContinuousScale;
-export 'src/scale/linear.dart' show LinearScale;
-export 'src/scale/ordinal.dart' show OrdinalScale;
-export 'src/scale/time.dart' show TimeScale;
+export 'src/scale/scale.dart' show Scale, ScaleConv;
+export 'src/scale/discrete.dart' show DiscreteScale, DiscreteScaleConv;
+export 'src/scale/continuous.dart' show ContinuousScale, ContinuousScaleConv;
+export 'src/scale/linear.dart' show LinearScale, LinearScaleConv;
+export 'src/scale/ordinal.dart' show OrdinalScale, OrdinalScaleConv;
+export 'src/scale/time.dart' show TimeScale, TimeScaleConv;
 
 export 'src/geom/element.dart' show GeomElement;
 export 'src/geom/function.dart' show FunctionElement;
@@ -141,7 +141,8 @@ export 'src/geom/interval.dart' show IntervalElement;
 export 'src/geom/line.dart' show LineElement;
 export 'src/geom/point.dart' show PointElement;
 export 'src/geom/polygon.dart' show PolygonElement;
-export 'src/geom/modifier/modifier.dart' show Modifier;
+export 'src/geom/modifier/modifier.dart'
+    show Modifier, GeomModifier, GeomModifierOp, ToGeomModifierOpParams;
 export 'src/geom/modifier/dodge.dart' show DodgeModifier;
 export 'src/geom/modifier/stack.dart' show StackModifier;
 export 'src/geom/modifier/jitter.dart' show JitterModifier;
@@ -201,7 +202,7 @@ export 'src/common/label.dart'
 export 'src/common/defaults.dart' show Defaults;
 export 'src/common/dim.dart' show Dim;
 
-export 'src/dataflow/tuple.dart' show Tuple, Aes;
+export 'src/dataflow/tuple.dart' show Tuple, Aes, AesGroups;
 
 export 'src/util/path.dart' show Paths;
 export 'package:path_drawing/path_drawing.dart' show DashOffset;

lib/src/dataflow/tuple.dart

@@ -66,7 +66,7 @@ class Aes {
   final Label? label;
 
   /// The size of the tuple.
-  final double? size;
+  double? size;
 
   /// The represent point of [position] points.
   Offset get representPoint => shape.representPoint(position);

lib/src/geom/modifier/dodge.dart

@@ -1,9 +1,9 @@
 import 'dart:ui';
 
+import 'package:graphic/src/algebra/varset.dart';
 import 'package:graphic/src/dataflow/tuple.dart';
 import 'package:graphic/src/scale/discrete.dart';
 import 'package:graphic/src/scale/scale.dart';
-import 'package:graphic/src/algebra/varset.dart';
 
 import 'modifier.dart';
 
@@ -34,6 +34,17 @@ class DodgeModifier extends Modifier {
       super == other &&
       ratio == other.ratio &&
       symmetric == other.symmetric;
+
+  @override
+  DodgeGeomModifierOp toGeomModifierOp(ToGeomModifierOpParams params) {
+    return DodgeGeomModifierOp({
+      'ratio': ratio,
+      'symmetric': symmetric ?? true,
+      'form': params.form,
+      'scales': params.scales,
+      'groups': params.groups,
+    });
+  }
 }
 
 /// The dodge geometry modifier.

lib/src/geom/modifier/jitter.dart

@@ -1,10 +1,10 @@
-import 'dart:ui';
 import 'dart:math';
+import 'dart:ui';
 
+import 'package:graphic/src/algebra/varset.dart';
 import 'package:graphic/src/dataflow/tuple.dart';
 import 'package:graphic/src/scale/discrete.dart';
 import 'package:graphic/src/scale/scale.dart';
-import 'package:graphic/src/algebra/varset.dart';
 
 import 'modifier.dart';
 
@@ -26,6 +26,15 @@ class JitterModifier extends Modifier {
   @override
   bool operator ==(Object other) =>
       other is JitterModifier && super == other && ratio == other.ratio;
+
+  @override
+  JitterGeomModifierOp toGeomModifierOp(ToGeomModifierOpParams params) {
+    return JitterGeomModifierOp({
+      'ratio': ratio ?? 0.5,
+      'form': params.form,
+      'scales': params.scales,
+    });
+  }
 }
 
 /// The jitter geometry modifier.

lib/src/geom/modifier/modifier.dart

@@ -1,6 +1,12 @@
+import 'package:graphic/graphic.dart';
 import 'package:graphic/src/common/modifier.dart' as common;
 import 'package:graphic/src/dataflow/operator.dart';
 import 'package:graphic/src/dataflow/tuple.dart';
+import 'package:graphic/src/scale/scale.dart';
+
+import '../../aes/position.dart';
+import '../../algebra/varset.dart';
+import '../../coord/coord.dart';
 
 /// The specification of a collision modifier.
 ///
@@ -9,6 +15,27 @@ import 'package:graphic/src/dataflow/tuple.dart';
 abstract class Modifier {
   @override
   bool operator ==(Object other) => other is Modifier;
+
+  GeomModifierOp<GeomModifier> toGeomModifierOp(ToGeomModifierOpParams params);
+}
+
+/// The only use of this class to pass parameters to [Modifier.toGeomModifierOp].
+/// A class is used, instead of named arguments, to avoid breaking changes when
+/// adding new fields to these parameters.
+class ToGeomModifierOpParams {
+  final AlgForm? form;
+  final ScaleConvOp scales;
+  final Operator<AesGroups> groups;
+  final OriginOp origin;
+  final CoordConvOp coord;
+
+  ToGeomModifierOpParams({
+    required this.form,
+    required this.scales,
+    required this.groups,
+    required this.origin,
+    required this.coord,
+  });
 }
 
 /// The base class of geometry modifiers.

lib/src/geom/modifier/stack.dart

@@ -16,6 +16,13 @@ import 'modifier.dart';
 class StackModifier extends Modifier {
   @override
   bool operator ==(Object other) => other is StackModifier && super == other;
+
+  @override
+  StackGeomModifierOp toGeomModifierOp(ToGeomModifierOpParams params) {
+    return StackGeomModifierOp({
+      'origin': params.origin,
+    });
+  }
 }
 
 /// The stack geometry modifier.

lib/src/geom/modifier/symmetric.dart

@@ -1,5 +1,5 @@
-import 'dart:ui';
 import 'dart:math';
+import 'dart:ui';
 
 import 'package:graphic/src/dataflow/tuple.dart';
 
@@ -15,6 +15,13 @@ class SymmetricModifier extends Modifier {
   @override
   bool operator ==(Object other) =>
       other is SymmetricModifier && super == other;
+
+  @override
+  SymmetricGeomModifierOp toGeomModifierOp(ToGeomModifierOpParams params) {
+    return SymmetricGeomModifierOp({
+      'origin': params.origin,
+    });
+  }
 }
 
 /// The symmetric geometry modifier.