diff --git a/src/picosvg/svg.py b/src/picosvg/svg.py
index ffd6e95..52a5bb1 100644
--- a/src/picosvg/svg.py
+++ b/src/picosvg/svg.py
@@ -19,11 +19,19 @@ import itertools
 from lxml import etree  # pytype: disable=import-error
 import re
 from typing import List, Optional, Tuple
-from picosvg.svg_meta import ntos, svgns, xlinkns, parse_css_declarations
+from picosvg.svg_meta import (
+    number_or_percentage,
+    ntos,
+    strip_ns,
+    svgns,
+    xlinkns,
+    parse_css_declarations,
+)
 from picosvg.svg_types import *
+from picosvg.svg_transform import Affine2D
 import numbers
 
-_ELEMENT_CLASSES = {
+_SHAPE_CLASSES = {
     "circle": SVGCircle,
     "ellipse": SVGEllipse,
     "line": SVGLine,
@@ -32,8 +40,17 @@ _ELEMENT_CLASSES = {
     "polyline": SVGPolyline,
     "rect": SVGRect,
 }
-_CLASS_ELEMENTS = {v: f"{{{svgns()}}}{k}" for k, v in _ELEMENT_CLASSES.items()}
-_ELEMENT_CLASSES.update({f"{{{svgns()}}}{k}": v for k, v in _ELEMENT_CLASSES.items()})
+_CLASS_ELEMENTS = {v: f"{{{svgns()}}}{k}" for k, v in _SHAPE_CLASSES.items()}
+_SHAPE_CLASSES.update({f"{{{svgns()}}}{k}": v for k, v in _SHAPE_CLASSES.items()})
+
+_GRADIENT_CLASSES = {
+    "linearGradient": SVGLinearGradient,
+    "radialGradient": SVGRadialGradient,
+}
+_GRADIENT_COORDS = {
+    "linearGradient": (("x1", "y1"), ("x2", "y2")),
+    "radialGradient": (("cx", "cy"), ("fx", "fy")),
+}
 
 _XLINK_TEMP = "xlink_"
 
@@ -46,6 +63,10 @@ _MAX_PCT_ERROR = 0.1
 _DEFAULT_DEFAULT_TOLERENCE = 0.1
 
 
+# Rounding for rewritten gradient matrices
+_GRADIENT_TRANSFORM_NDIGITS = 6
+
+
 def _xlink_href_attr_name() -> str:
     return f"{{{xlinkns()}}}href"
 
@@ -104,9 +125,10 @@ def _field_name(attr_name):
 
 
 def from_element(el):
-    if el.tag not in _ELEMENT_CLASSES:
+    if el.tag not in _SHAPE_CLASSES:
         raise ValueError(f"Bad tag <{el.tag}>")
-    data_type = _ELEMENT_CLASSES[el.tag]
+    data_type = _SHAPE_CLASSES[el.tag]
+    parse_fn = getattr(data_type, "from_element", None)
     args = {
         f.name: f.type(el.attrib[_attr_name(f.name)])
         for f in dataclasses.fields(data_type)
@@ -148,8 +170,9 @@ class SVG:
         if self.elements:
             return self.elements
         elements = []
+        view_box = self.view_box()
         for el in self.svg_root.iter("*"):
-            if el.tag not in _ELEMENT_CLASSES:
+            if el.tag not in _SHAPE_CLASSES:
                 continue
             elements.append((el, (from_element(el),)))
         self.elements = elements
@@ -679,17 +702,89 @@ class SVG:
 
         return self
 
+    def _select_gradients(self):
+        return self.xpath(" | ".join(f"//svg:{tag}" for tag in _GRADIENT_CLASSES))
+
+    def _collect_gradients(self, inplace=False):
+        if not inplace:
+            svg = SVG(copy.deepcopy(self.svg_root))
+            svg._collect_gradients(inplace=False)
+            return svg
+
+        # Collect gradients; remove other defs
+        defs = etree.Element(f"{{{svgns()}}}defs", nsmap=self.svg_root.nsmap)
+        for gradient in self._select_gradients():
+            gradient.getparent().remove(gradient)
+            defs.append(gradient)
+
+        for def_el in [e for e in self.xpath("//svg:defs")]:
+            def_el.getparent().remove(def_el)
+
+        self.svg_root.insert(0, defs)
+
+    def _apply_gradient_translation(self, inplace=False):
+        if not inplace:
+            svg = SVG(copy.deepcopy(self.svg_root))
+            svg._apply_gradient_translation(inplace=True)
+            return svg
+
+        for el in self._select_gradients():
+            gradient = _GRADIENT_CLASSES[strip_ns(el.tag)].from_element(
+                el, self.view_box()
+            )
+            affine = gradient.gradientTransform
+            a, b, c, d, dx, dy = affine
+            if (dx, dy) == (0, 0):
+                continue
+            affine_prime = affine._replace(e=0, f=0)
+
+            for x_attr, y_attr in _GRADIENT_COORDS[strip_ns(el.tag)]:
+                # if at default just ignore
+                if x_attr not in el.attrib and y_attr not in el.attrib:
+                    continue
+                x = getattr(gradient, x_attr)
+                y = getattr(gradient, y_attr)
+
+                # We need x`, y` such that matrix a b c d 0 0 yields same
+                # result as x,y with a b c d e f
+                # That is:
+                # 1)  ax` + cy` + 0 = ax + cy + e
+                # 2)  bx` + dy` + 0 = bx + dy + f
+                #                   ^ rhs is a known scalar; we'll call r1, r2
+                # multiply 1) by b/a so when subtracted from 2) we eliminate x`
+                # 1)  bx` + (b/a)cy` = (b/a) * r1
+                # 2) - 1)  bx` - bx` + dy` - (b/a)cy` = r2 - (b/a) * r1
+                #         y` = (r2 - (b/a) * r1) / (d - (b/a)c)
+                r1, r2 = affine.map_point((x, y))
+                assert r1 == a * x + c * y + dx
+                assert r2 == b * x + d * y + dy
+                y_prime = (r2 - r1 * b / a) / (d - b * c / a)
+
+                # Sub y` into 1)
+                # 1) x` = (r1 - cy`) / a
+                x_prime = (r1 - c * y_prime) / a
+
+                # sanity check: a`(x`, y`) should be a(x, y)
+                p = affine.map_point((x, y))
+                p_prime = affine_prime.map_point((x_prime, y_prime))
+                assert p.almost_equals(p_prime)
+
+                el.attrib[x_attr] = ntos(round(x_prime, _GRADIENT_TRANSFORM_NDIGITS))
+                el.attrib[y_attr] = ntos(round(y_prime, _GRADIENT_TRANSFORM_NDIGITS))
+
+            if affine_prime != Affine2D.identity():
+                el.attrib["gradientTransform"] = (
+                    "matrix(" + " ".join(ntos(v) for v in affine_prime) + ")"
+                )
+            else:
+                del el.attrib["gradientTransform"]
+
     def checkpicosvg(self):
         """Check for nano violations, return xpaths to bad elements.
 
         If result sequence empty then this is a valid picosvg.
         """
 
-        def _strip_ns(tagname):
-            if "}" in tagname:
-                return tagname[tagname.index("}") + 1 :]
-            return tagname
-
         self._update_etree()
 
         errors = []
@@ -705,7 +800,7 @@ class SVG:
         frontier = [(0, self.svg_root, "")]
         while frontier:
             el_idx, el, parent_path = frontier.pop(0)
-            el_tag = _strip_ns(el.tag)
+            el_tag = strip_ns(el.tag)
             el_path = f"{parent_path}/{el_tag}[{el_idx}]"
 
             if not any((re.match(pat, el_path) for pat in path_whitelist)):
@@ -742,16 +837,8 @@ class SVG:
         self.absolute(inplace=True)
         self.round_floats(ndigits, inplace=True)
 
-        # Collect gradients; remove other defs
-        defs = etree.Element(f"{{{svgns()}}}defs", nsmap=self.svg_root.nsmap)
-        for gradient in self.xpath("//svg:linearGradient | //svg:radialGradient"):
-            gradient.getparent().remove(gradient)
-            defs.append(gradient)
-
-        for def_el in [e for e in self.xpath("//svg:defs")]:
-            def_el.getparent().remove(def_el)
-
-        self.svg_root.insert(0, defs)
+        self._apply_gradient_translation(inplace=True)
+        self._collect_gradients(inplace=True)
 
         nano_violations = self.checkpicosvg()
         if nano_violations:
diff --git a/src/picosvg/svg_meta.py b/src/picosvg/svg_meta.py
index 253d333..fea4c73 100644
--- a/src/picosvg/svg_meta.py
+++ b/src/picosvg/svg_meta.py
@@ -36,6 +36,12 @@ def xlinkns():
     return "http://www.w3.org/1999/xlink"
 
 
+def strip_ns(tagname):
+    if "}" in tagname:
+        return tagname[tagname.index("}") + 1 :]
+    return tagname
+
+
 # https://www.w3.org/TR/SVG11/paths.html#PathData
 _CMD_ARGS = {
     "m": 2,
@@ -100,6 +106,10 @@ def ntos(n: float) -> str:
     return str(int(n)) if isinstance(n, float) and n.is_integer() else str(n)
 
 
+def number_or_percentage(s: str, scale=1) -> float:
+    return float(s[:-1]) / 100 * scale if s.endswith("%") else float(s)
+
+
 def path_segment(cmd, *args):
     # put commas between coords, spaces otherwise, author readability pref
     args_per_cmd = check_cmd(cmd, args)
diff --git a/src/picosvg/svg_types.py b/src/picosvg/svg_types.py
index b8ebd5e..3565354 100644
--- a/src/picosvg/svg_types.py
+++ b/src/picosvg/svg_types.py
@@ -15,7 +15,16 @@
 import copy
 import dataclasses
 from picosvg.geometric_types import Point, Rect
-from picosvg import svg_meta
+from picosvg.svg_meta import (
+    check_cmd,
+    cmd_coords,
+    number_or_percentage,
+    parse_css_declarations,
+    path_segment,
+    strip_ns,
+    SVGCommand,
+    SVGCommandSeq,
+)
 from picosvg import svg_pathops
 from picosvg.arc_to_cubic import arc_to_cubic
 from picosvg.svg_path_iter import parse_svg_path
@@ -45,7 +54,7 @@ def _explicit_lines_callback(subpath_start, curr_pos, cmd, args, *_):
 
 
 def _relative_to_absolute(curr_pos, cmd, args):
-    x_coord_idxs, y_coord_idxs = svg_meta.cmd_coords(cmd)
+    x_coord_idxs, y_coord_idxs = cmd_coords(cmd)
     if cmd.islower():
         cmd = cmd.upper()
         args = list(args)  # we'd like to mutate 'em
@@ -59,7 +68,7 @@ def _relative_to_absolute(curr_pos, cmd, args):
 
 def _next_pos(curr_pos, cmd, cmd_args):
     # update current position
-    x_coord_idxs, y_coord_idxs = svg_meta.cmd_coords(cmd)
+    x_coord_idxs, y_coord_idxs = cmd_coords(cmd)
     new_x, new_y = curr_pos
     if cmd.isupper():
         if x_coord_idxs:
@@ -79,7 +88,7 @@ def _move_endpoint(curr_pos, cmd, cmd_args, new_endpoint):
     # we need to be able to alter both axes
     ((cmd, cmd_args),) = _explicit_lines_callback(None, curr_pos, cmd, cmd_args)
 
-    x_coord_idxs, y_coord_idxs = svg_meta.cmd_coords(cmd)
+    x_coord_idxs, y_coord_idxs = cmd_coords(cmd)
     cmd_args = list(cmd_args)  # we'd like to mutate
     new_x, new_y = new_endpoint
     if cmd.islower():
@@ -179,7 +188,7 @@ class SVGShape:
     def as_path(self) -> "SVGPath":
         raise NotImplementedError("You should implement as_path")
 
-    def as_cmd_seq(self) -> svg_meta.SVGCommandSeq:
+    def as_cmd_seq(self) -> SVGCommandSeq:
         return (
             self.as_path()
             .explicit_lines()  # hHvV => lL
@@ -193,7 +202,7 @@ class SVGShape:
         # only meaningful for path, which overrides
         return self
 
-    def stroke_commands(self, tolerance) -> Generator[svg_meta.SVGCommand, None, None]:
+    def stroke_commands(self, tolerance) -> Generator[SVGCommand, None, None]:
         return svg_pathops.stroke(
             self.as_cmd_seq(),
             self.stroke_linecap,
@@ -217,7 +226,7 @@ class SVGShape:
                 f.name.replace("_", "-"): f.type for f in dataclasses.fields(self)
             }
             raw_attrs = {}
-            unparsed_style = svg_meta.parse_css_declarations(
+            unparsed_style = parse_css_declarations(
                 target.style, raw_attrs, property_names=attr_types.keys()
             )
             for attr_name, attr_value in raw_attrs.items():
@@ -245,7 +254,7 @@ class SVGShape:
 
 # https://www.w3.org/TR/SVG11/paths.html#PathElement
 @dataclasses.dataclass
-class SVGPath(SVGShape, svg_meta.SVGCommandSeq):
+class SVGPath(SVGShape, SVGCommandSeq):
     d: str = ""
 
     def __init__(self, **kwargs):
@@ -258,7 +267,7 @@ class SVGPath(SVGShape, svg_meta.SVGCommandSeq):
         self.d += path_snippet
 
     def _add_cmd(self, cmd, *args):
-        self._add(svg_meta.path_segment(cmd, *args))
+        self._add(path_segment(cmd, *args))
 
     def M(self, *args):
         self._add_cmd("M", *args)
@@ -267,7 +276,7 @@ class SVGPath(SVGShape, svg_meta.SVGCommandSeq):
         self._add_cmd("m", *args)
 
     def _arc(self, c, rx, ry, x, y, large_arc):
-        self._add(svg_meta.path_segment(c, rx, ry, 0, large_arc, 1, x, y))
+        self._add(path_segment(c, rx, ry, 0, large_arc, 1, x, y))
 
     def A(self, rx, ry, x, y, large_arc=0):
         self._arc("A", rx, ry, x, y, large_arc)
@@ -332,7 +341,7 @@ class SVGPath(SVGShape, svg_meta.SVGCommandSeq):
 
         # iteration gives us exploded commands
         for idx, (cmd, args) in enumerate(self):
-            svg_meta.check_cmd(cmd, args)
+            check_cmd(cmd, args)
             if idx == 0 and cmd == "m":
                 cmd = "M"
 
@@ -366,7 +375,7 @@ class SVGPath(SVGShape, svg_meta.SVGCommandSeq):
             # Shift the absolute parts and call it a day.
             if cmd.islower():
                 return ((cmd, args),)
-            x_coord_idxs, y_coord_idxs = svg_meta.cmd_coords(cmd)
+            x_coord_idxs, y_coord_idxs = cmd_coords(cmd)
             args = list(args)  # we'd like to mutate 'em
             for x_coord_idx in x_coord_idxs:
                 args[x_coord_idx] += dx
@@ -485,13 +494,11 @@ class SVGPath(SVGShape, svg_meta.SVGCommandSeq):
         return target
 
     @classmethod
-    def from_commands(
-        cls, svg_cmds: Generator[svg_meta.SVGCommand, None, None]
-    ) -> "SVGPath":
+    def from_commands(cls, svg_cmds: Generator[SVGCommand, None, None]) -> "SVGPath":
         return cls().update_path(svg_cmds, inplace=True)
 
     def update_path(
-        self, svg_cmds: Generator[svg_meta.SVGCommand, None, None], inplace=False
+        self, svg_cmds: Generator[SVGCommand, None, None], inplace=False
     ) -> "SVGPath":
         target = self
         if not inplace:
@@ -637,6 +644,90 @@ class SVGRect(SVGShape):
         return path
 
 
+def _get_gradient_units_relative_scale(grad_el, view_box):
+    gradient_units = grad_el.attrib.get("gradientUnits", "objectBoundingBox")
+    if gradient_units == "userSpaceOnUse":
+        # For gradientUnits="userSpaceOnUse", percentages represent values relative to
+        # the current viewport.
+        return view_box
+    elif gradient_units == "objectBoundingBox":
+        # For gradientUnits="objectBoundingBox", percentages represent values relative
+        # to the object bounding box. The latter defines an abstract coordinate system
+        # with origin at (0,0) and a nominal width and height = 1.
+        return Rect(0, 0, 1, 1)
+    else:
+        raise ValueError(
+            f'{strip_ns(grad_el.tag)} gradientUnits="{gradient_units}" not supported'
+        )
+
+
+def _parse_common_gradient_parts(gradient, el, view_box):
+    self = gradient
+    self.gradientUnits = _get_gradient_units_relative_scale(el, view_box)
+    if "gradientTransform" in el.attrib:
+        self.gradientTransform = Affine2D.fromstring(el.attrib["gradientTransform"])
+    if "spreadMethod" in el.attrib:
+        self.spreadMethod = el.attrib["spreadMethod"]
+    return self.gradientUnits.w, self.gradientUnits.h
+
+
+# https://developer.mozilla.org/en-US/docs/Web/SVG/Element/linearGradient
+# Should be parsed with from_element
+@dataclasses.dataclass
+class SVGLinearGradient:
+    x1: float = 0.0
+    x2: float = 0.0
+    y1: float = 0.0
+    y2: float = 0.0
+    gradientUnits: Rect = Rect(0, 0, 1, 1)
+    gradientTransform: Affine2D = Affine2D.identity()
+    spreadMethod: str = "pad"
+
+    @staticmethod
+    def from_element(el, view_box) -> "SVGLinearGradient":
+        self = SVGLinearGradient()
+        width, height = _parse_common_gradient_parts(self, el, view_box)
+
+        self.x1 = number_or_percentage(el.attrib.get("x1", "0%"), width)
+        self.y1 = number_or_percentage(el.attrib.get("y1", "0%"), height)
+        self.x2 = number_or_percentage(el.attrib.get("x2", "100%"), width)
+        self.y2 = number_or_percentage(el.attrib.get("y2", "0%"), height)
+        return self
+
+
+# https://developer.mozilla.org/en-US/docs/Web/SVG/Element/radialGradient
+# Should be parsed with from_element
+@dataclasses.dataclass
+class SVGRadialGradient:
+    cx: float = 0.0
+    cy: float = 0.0
+    r: float = 0.0
+    fr: float = 0.0
+    fx: float = 0.0
+    fy: float = 0.0
+    gradientUnits: Rect = Rect(0, 0, 1, 1)
+    gradientTransform: Affine2D = Affine2D.identity()
+    spreadMethod: str = "pad"
+
+    @staticmethod
+    def from_element(el, view_box) -> "SVGRadialGradient":
+        self = SVGRadialGradient()
+        width, height = _parse_common_gradient_parts(self, el, view_box)
+
+        self.cx = number_or_percentage(el.attrib.get("cx", "50%"), width)
+        self.cy = number_or_percentage(el.attrib.get("cy", "50%"), height)
+        self.r = number_or_percentage(el.attrib.get("r", "50%"), width)
+
+        raw_fx = el.attrib.get("fx")
+        self.fx = number_or_percentage(raw_fx, width) if raw_fx is not None else self.cx
+        raw_fy = el.attrib.get("fy")
+        self.fy = (
+            number_or_percentage(raw_fy, height) if raw_fy is not None else self.cy
+        )
+        self.fr = number_or_percentage(el.attrib.get("fr", "0%"), width)
+        return self
+
+
 def union(shapes: Iterable[SVGShape]) -> SVGPath:
     return SVGPath.from_commands(
         svg_pathops.union(

diff --git a/tests/svg_test.py b/tests/svg_test.py
index 965d0ca..2b781b5 100644
--- a/tests/svg_test.py
+++ b/tests/svg_test.py
@@ -17,7 +17,7 @@ from lxml import etree
 import os
 import pytest
 from picosvg.svg import SVG
-from picosvg import svg_meta
+from picosvg.svg_meta import strip_ns, parse_css_declarations
 from svg_test_helpers import *
 
 
@@ -380,7 +380,7 @@ def test_parse_css_declarations(
     style, property_names, expected_output, expected_unparsed
 ):
     output = {}
-    unparsed = svg_meta.parse_css_declarations(style, output, property_names)
+    unparsed = parse_css_declarations(style, output, property_names)
     assert output == expected_output
     assert unparsed == expected_unparsed
 
@@ -388,7 +388,7 @@ def test_parse_css_declarations(
 @pytest.mark.parametrize("style", ["foo;bar;", "foo:bar:baz;"])
 def test_parse_css_declarations_invalid(style):
     with pytest.raises(ValueError, match="Invalid CSS declaration syntax"):
-        svg_meta.parse_css_declarations(style, {})
+        parse_css_declarations(style, {})
 
 
 @pytest.mark.parametrize(
@@ -403,3 +403,47 @@ def test_apply_style_attributes(actual, expected_result):
         expected_result,
         lambda svg: svg.shapes() and svg.apply_style_attributes(),
     )
+
+
+@pytest.mark.parametrize(
+    "gradient_string, expected_result",
+    [
+        # No transform, no change
+        (
+            '<linearGradient id="c" x1="63.85" x2="63.85" y1="4245" y2="4137.3" gradientUnits="userSpaceOnUse"/>',
+            '<linearGradient id="c" x1="63.85" x2="63.85" y1="4245" y2="4137.3" gradientUnits="userSpaceOnUse"/>',
+        ),
+        # Real example from emoji_u1f392.svg w/ dx changed from 0 to 1
+        # scale, translate
+        (
+            '<linearGradient id="c" x1="63.85" x2="63.85" y1="4245" y2="4137.3" gradientTransform="translate(1 -4122)" gradientUnits="userSpaceOnUse"/>',
+            '<linearGradient id="c" x1="64.85" x2="64.85" y1="123" y2="15.3" gradientUnits="userSpaceOnUse"/>',
+        ),
+        # Real example from emoji_u1f392.svg w/sx changed from 1 to 0.5
+        # scale, translate
+        (
+            '<radialGradient id="b" cx="63.523" cy="12368" r="53.477" gradientTransform="matrix(.5 0 0 .2631 0 -3150)" gradientUnits="userSpaceOnUse"/>',
+            '<radialGradient id="b" cx="63.523" cy="395.366021" r="53.477" gradientTransform="matrix(0.5 0 0 0.2631 0 0)" gradientUnits="userSpaceOnUse"/>',
+        ),
+        # Real example from emoji_u1f44d.svg
+        # Using all 6 parts
+        (
+            '<radialGradient id="d" cx="2459.4" cy="-319.18" r="20.331" gradientTransform="matrix(-1.3883 .0794 -.0374 -.6794 3505.4 -353.39)" gradientUnits="userSpaceOnUse"/>',
+            '<radialGradient id="d" cx="-71.60264" cy="-94.82264" r="20.331" gradientTransform="matrix(-1.3883 0.0794 -0.0374 -0.6794 0 0)" gradientUnits="userSpaceOnUse"/>',
+        ),
+    ],
+)
+def test_apply_gradient_translation(gradient_string, expected_result):
+    svg_string = (
+        '<svg version="1.1" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 128 128">'
+        + gradient_string
+        + "</svg>"
+    )
+    svg = SVG.fromstring(svg_string)._apply_gradient_translation()
+    el = svg.xpath_one("//svg:linearGradient | //svg:radialGradient")
+
+    for node in svg.svg_root.getiterator():
+        node.tag = etree.QName(node).localname
+    etree.cleanup_namespaces(svg.svg_root)
+
+    assert etree.tostring(el).decode("utf-8") == expected_result

Apply gradient translation
Noto has things like:

```xml
<linearGradient id="c" x1="63.85" x2="63.85" y1="4245" y2="4137.3" gradientTransform="translate(0 -4122)" gradientUnits="userSpaceOnUse">
<radialGradient id="b" cx="63.523" cy="12368" r="53.477" gradientTransform="matrix(1 0 0 .2631 0 -3150)" gradientUnits="userSpaceOnUse">
```

At minimum, just apply the translate transform on a gradient. Perhaps just apply the whole transform, need to think about that.

Credit to @anthrotype for spotting this pattern.
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