Merge pull request #462 from psychon/gears.matrix2

Implement full matrix operations in gears.matrix

Closes https://github.com/awesomeWM/awesome/pull/462.

lib/gears/matrix.lua

@@ -1,50 +1,166 @@
 ---------------------------------------------------------------------------
+-- An implementation of matrices for describing and working with affine
+-- transformations.
 -- @author Uli Schlachter
 -- @copyright 2015 Uli Schlachter
 -- @release @AWESOME_VERSION@
--- @module gears.matrix
+-- @classmod gears.matrix
 ---------------------------------------------------------------------------
 
 local cairo = require("lgi").cairo
 local debug = require("gears.debug")
 local matrix = {}
 
---- Copy a cairo matrix
+-- Metatable for matrix instances. This is set up near the end of the file.
--- @param matrix The matrix to copy.
+local matrix_mt = {}
--- @return A copy of the given cairo matrix.
+
-function matrix.copy(matrix)
+--- Create a new matrix instance
-    debug.assert(cairo.Matrix:is_type_of(matrix), "Argument should be a cairo matrix")
+-- @tparam number xx The xx transformation part.
-    local ret = cairo.Matrix()
+-- @tparam number yx The yx transformation part.
-    ret:init(matrix.xx, matrix.yx, matrix.xy, matrix.yy, matrix.x0, matrix.y0)
+-- @tparam number xy The xy transformation part.
-    return ret
+-- @tparam number yy The yy transformation part.
+-- @tparam number x0 The x0 transformation part.
+-- @tparam number y0 The y0 transformation part.
+-- @return A new matrix describing the given transformation.
+function matrix.create(xx, yx, xy, yy, x0, y0)
+    return setmetatable({
+        xx = xx, xy = xy, x0 = x0,
+        yx = yx, yy = yy, y0 = y0
+    }, matrix_mt)
 end
 
---- Check if two cairo matrices are equal
+--- Create a new translation matrix
--- @param m1 The first matrix to compare with.
+-- @tparam number x The translation in x direction.
--- @param m2 The second matrix to compare with.
+-- @tparam number y The translation in y direction.
--- @return True if they are equal.
+-- @return A new matrix describing the given transformation.
-function matrix.equals(m1, m2)
+function matrix.create_translate(x, y)
+    return matrix.create(1, 0, 0, 1, x, y)
+end
+
+--- Create a new scaling matrix
+-- @tparam number sx The scaling in x direction.
+-- @tparam number sy The scaling in y direction.
+-- @return A new matrix describing the given transformation.
+function matrix.create_scale(sx, sy)
+    return matrix.create(sx, 0, 0, sy, 0, 0)
+end
+
+--- Create a new rotation matrix
+-- @tparam number angle The angle of the rotation in radians.
+-- @return A new matrix describing the given transformation.
+function matrix.create_rotate(angle)
+    local c, s = math.cos(angle), math.sin(angle)
+    return matrix.create(c, s, -s, c, 0, 0)
+end
+
+--- Translate this matrix
+-- @tparam number x The translation in x direction.
+-- @tparam number y The translation in y direction.
+-- @return A new matrix describing the new transformation.
+function matrix:translate(x, y)
+    return matrix.create_translate(x, y):multiply(self)
+end
+
+--- Scale this matrix
+-- @tparam number sx The scaling in x direction.
+-- @tparam number sy The scaling in y direction.
+-- @return A new matrix describing the new transformation.
+function matrix:scale(sx, sy)
+    return matrix.create_scale(sx, sy):multiply(self)
+end
+
+--- Rotate this matrix
+-- @tparam number angle The angle of the rotation in radians.
+-- @return A new matrix describing the new transformation.
+function matrix:rotate(angle)
+    return matrix.create_rotate(angle):multiply(self)
+end
+
+--- Invert this matrix
+-- @return A new matrix describing the inverse transformation.
+function matrix:invert()
+    -- Beware of math! (I just copied the algorithm from cairo's source code)
+    local a, b, c, d, x0, y0 = self.xx, self.yx, self.xy, self.yy, self.x0, self.y0
+    local inv_det = 1/(a*d - b*c)
+    return matrix.create(inv_det * d, inv_det * -b,
+            inv_det * -c, inv_det * a,
+            inv_det * (c * y0 - d * x0), inv_det * (b * x0 - a * y0))
+end
+
+--- Multiply this matrix with another matrix.
+-- The resulting matrix describes a transformation that is equivalent to first
+-- applying this transformation and then the transformation from `other`.
+-- Note that this function can also be called by directly multiplicating two
+-- matrix instances: `a * b == a:multiply(b)`.
+-- @tparam gears.matrix|cairo.Matrix other The other matrix to multiply with.
+-- @return The multiplication result.
+function matrix:multiply(other)
+    return matrix.create(self.xx * other.xx + self.yx * other.xy,
+            self.xx * other.yx + self.yx * other.yy,
+            self.xy * other.xx + self.yy * other.xy,
+            self.xy * other.yx + self.yy * other.yy,
+            self.x0 * other.xx + self.y0 * other.xy + other.x0,
+            self.x0 * other.yx + self.y0 * other.yy + other.y0)
+end
+
+--- Check if two matrices are equal.
+-- Note that this function cal also be called by directly comparing two matrix
+-- instances: `a == b`.
+-- @tparam gears.matrix|cairo.Matrix other The matrix to compare with.
+-- @return True if this and the other matrix are equal.
+function matrix:equals(other)
     for _, k in pairs{ "xx", "xy", "yx", "yy", "x0", "y0" } do
-        if m1[k] ~= m2[k] then
+        if self[k] ~= other[k] then
             return false
         end
     end
     return true
 end
 
+--- Get a string representation of this matrix
+-- @return A string showing this matrix in column form.
+function matrix:tostring()
+    return string.format("[[%g, %g], [%g, %g], [%g, %g]]",
+            self.xx, self.yx, self.xy,
+            self.yy, self.x0, self.y0)
+end
+
+--- Transform a distance by this matrix.
+-- The difference to @{matrix:transform_point} is that the translation part of
+-- this matrix is ignored.
+-- @tparam number x The x coordinate of the point.
+-- @tparam number y The y coordinate of the point.
+-- @treturn number The x coordinate of the transformed point.
+-- @treturn number The x coordinate of the transformed point.
+function matrix:transform_distance(x, y)
+    return self.xx * x + self.xy * y, self.yx * x + self.yy * y
+end
+
+--- Transform a point by this matrix.
+-- @tparam number x The x coordinate of the point.
+-- @tparam number y The y coordinate of the point.
+-- @treturn number The x coordinate of the transformed point.
+-- @treturn number The x coordinate of the transformed point.
+function matrix:transform_point(x, y)
+    local x, y = self:transform_distance(x, y)
+    return self.x0 + x, self.y0 + y
+end
+
 --- Calculate a bounding rectangle for transforming a rectangle by a matrix.
--- @param matrix The cairo matrix that describes the transformation.
+-- @tparam number x The x coordinate of the rectangle.
--- @param x The x coordinate of the rectangle.
+-- @tparam number y The y coordinate of the rectangle.
--- @param y The y coordinate of the rectangle.
+-- @tparam number width The width of the rectangle.
--- @param width The width of the rectangle.
+-- @tparam number height The height of the rectangle.
--- @param height The height of the rectangle.
+-- @treturn number X coordinate of the bounding rectangle.
--- @return The x, y, width and height of the bounding rectangle.
+-- @treturn number Y coordinate of the bounding rectangle.
-function matrix.transform_rectangle(matrix, x, y, width, height)
+-- @treturn number Width of the bounding rectangle.
+-- @treturn number Height of the bounding rectangle.
+function matrix:transform_rectangle(x, y, width, height)
     -- Transform all four corners of the rectangle
-    local x1, y1 = matrix:transform_point(x, y)
+    local x1, y1 = self:transform_point(x, y)
-    local x2, y2 = matrix:transform_point(x, y + height)
+    local x2, y2 = self:transform_point(x, y + height)
-    local x3, y3 = matrix:transform_point(x + width, y + height)
+    local x3, y3 = self:transform_point(x + width, y + height)
-    local x4, y4 = matrix:transform_point(x + width, y)
+    local x4, y4 = self:transform_point(x + width, y)
     -- Find the extremal points of the result
     local x = math.min(x1, x2, x3, x4)
     local y = math.min(y1, y2, y3, y4)
@@ -54,6 +170,30 @@ function matrix.transform_rectangle(matrix, x, y, width, height)
     return x, y, width, height
 end
 
+--- Convert to a cairo matrix
+-- @treturn cairo.Matrix A cairo matrix describing the same transformation.
+function matrix:to_cairo_matrix()
+    local ret = cairo.Matrix()
+    ret:init(self.xx, self.yx, self.xy, self.yy, self.x0, self.y0)
+    return ret
+end
+
+--- Convert to a cairo matrix
+-- @tparam cairo.Matrix mat A cairo matrix describing the sought transformation
+-- @treturn gears.matrix A matrix instance describing the same transformation.
+function matrix.from_cairo_matrix(mat)
+    return matrix.create(mat.xx, mat.yx, mat.xy, mat.yy, mat.x0, mat.y0)
+end
+
+matrix_mt.__index = matrix
+matrix_mt.__newindex = error
+matrix_mt.__eq = matrix.equals
+matrix_mt.__mul = matrix.multiply
+matrix_mt.__tostring = matrix.tostring
+
+--- A constant for the identity matrix.
+matrix.identity = matrix.create(1, 0, 0, 1, 0, 0)
+
 return matrix
 
 -- vim: filetype=lua:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:textwidth=80

lib/wibox/hierarchy.lua

@@ -37,11 +37,8 @@ local function hierarchy_new(context, widget, width, height, redraw_callback, la
     widget:weak_connect_signal("widget::layout_changed", result._layout)
 
     for _, w in ipairs(children or {}) do
-        local to_dev = cairo.Matrix.create_identity()
-        to_dev:multiply(matrix_to_device, w._matrix)
-
         local r = hierarchy_new(context, w._widget, w._width, w._height, redraw_callback, layout_callback,
-                callback_arg, matrix.copy(w._matrix), to_dev)
+                callback_arg, w._matrix, matrix_to_device * w._matrix)
         table.insert(result._children, r)
 
         -- Update our drawing extents
@@ -82,7 +79,7 @@ end
 -- @return A new widget hierarchy
 function hierarchy.new(context, widget, width, height, redraw_callback, layout_callback, callback_arg)
     return hierarchy_new(context, widget, width, height, redraw_callback, layout_callback, callback_arg,
-            cairo.Matrix.create_identity(), cairo.Matrix.create_identity())
+            matrix.identity, matrix.identity)
 end
 
 --- Get the widget that this hierarchy manages.
@@ -90,38 +87,36 @@ function hierarchy:get_widget()
     return self._widget
 end
 
---- Get a cairo matrix that transforms to the parent's coordinate space from
+--- Get a matrix that transforms to the parent's coordinate space from this
--- this hierarchy's coordinate system.
+-- hierarchy's coordinate system.
--- @return A cairo matrix describing the transformation.
+-- @return A matrix describing the transformation.
 function hierarchy:get_matrix_to_parent()
-    return matrix.copy(self._matrix)
+    return self._matrix
 end
 
---- Get a cairo matrix that transforms to the base of this hierarchy's
+--- Get a matrix that transforms to the base of this hierarchy's coordinate
--- coordinate system (aka the coordinate system of the device that this
+-- system (aka the coordinate system of the device that this
 -- hierarchy is applied upon) from this hierarchy's coordinate system.
--- @return A cairo matrix describing the transformation.
+-- @return A matrix describing the transformation.
 function hierarchy:get_matrix_to_device()
-    return matrix.copy(self._matrix_to_device)
+    return self._matrix_to_device
 end
 
---- Get a cairo matrix that transforms from the parent's coordinate space into
+--- Get a matrix that transforms from the parent's coordinate space into this
--- this hierarchy's coordinate system.
+-- hierarchy's coordinate system.
--- @return A cairo matrix describing the transformation.
+-- @return A matrix describing the transformation.
 function hierarchy:get_matrix_from_parent()
     local m = self:get_matrix_to_parent()
-    m:invert()
+    return m:invert()
-    return m
 end
 
---- Get a cairo matrix that transforms from the base of this hierarchy's
+--- Get a matrix that transforms from the base of this hierarchy's coordinate
--- coordinate system (aka the coordinate system of the device that this
+-- system (aka the coordinate system of the device that this
 -- hierarchy is applied upon) into this hierarchy's coordinate system.
--- @return A cairo matrix describing the transformation.
+-- @return A matrix describing the transformation.
 function hierarchy:get_matrix_from_device()
     local m = self:get_matrix_to_device()
-    m:invert()
+    return m:invert()
-    return m
 end
 
 --- Get the extents that this hierarchy possibly draws to (in the current coordinate space).
@@ -198,7 +193,7 @@ function hierarchy:draw(context, cr)
     end
 
     cr:save()
-    cr:transform(self:get_matrix_to_parent())
+    cr:transform(self:get_matrix_to_parent():to_cairo_matrix())
 
     -- Clip to the draw extents
     cr:rectangle(self:get_draw_extents())

lib/wibox/layout/mirror.lua

@@ -11,7 +11,7 @@ local pairs = pairs
 local ipairs = ipairs
 local setmetatable = setmetatable
 local base = require("wibox.widget.base")
-local Matrix = require("lgi").cairo.Matrix
+local matrix = require("gears.matrix")
 
 local mirror = { mt = {} }
 
@@ -23,7 +23,7 @@ function mirror:layout(context, cr, width, height)
         return
     end
 
-    local m = Matrix.create_identity()
+    local m = matrix.identity
     local t = { x = 0, y = 0 } -- translation
     local s = { x = 1, y = 1 } -- scale
     if self.horizontal then
@@ -34,8 +34,8 @@ function mirror:layout(context, cr, width, height)
         t.x = width
         s.x = -1
     end
-    m:translate(t.x, t.y)
+    m = m:translate(t.x, t.y)
-    m:scale(s.x, s.y)
+    m = m:scale(s.x, s.y)
 
     return base.place_widget_via_matrix(widget, m, width, height)
 end

lib/wibox/layout/rotate.lua

@@ -12,7 +12,7 @@ local type = type
 local setmetatable = setmetatable
 local tostring = tostring
 local base = require("wibox.widget.base")
-local Matrix = require("lgi").cairo.Matrix
+local matrix = require("gears.matrix")
 
 local rotate = { mt = {} }
 
@@ -32,16 +32,16 @@ function rotate:layout(context, width, height)
 
     local dir = self:get_direction()
 
-    local m = Matrix.create_identity()
+    local m = matrix.identity
     if dir == "west" then
-        m:rotate(pi / 2)
+        m = m:rotate(pi / 2)
-        m:translate(0, -width)
+        m = m:translate(0, -width)
     elseif dir == "south" then
-        m:rotate(pi)
+        m = m:rotate(pi)
-        m:translate(-width, -height)
+        m = m:translate(-width, -height)
     elseif dir == "east" then
-        m:rotate(3 * pi / 2)
+        m = m:rotate(3 * pi / 2)
-        m:translate(-height, 0)
+        m = m:translate(-height, 0)
     end
 
     -- Since we rotated, we might have to swap width and height.

lib/wibox/widget/base.lua

@@ -9,7 +9,6 @@ local debug = require("gears.debug")
 local object = require("gears.object")
 local cache = require("gears.cache")
 local matrix = require("gears.matrix")
-local Matrix = require("lgi").cairo.Matrix
 local setmetatable = setmetatable
 local pairs = pairs
 local type = type
@@ -204,8 +203,8 @@ end
 --- Create widget placement information. This should be used for a widget's
 -- `:layout()` callback.
 -- @param widget The widget that should be placed.
--- @param mat A cairo matrix transforming from the parent widget's coordinate
+-- @param mat A matrix transforming from the parent widget's coordinate
---        system. For example, use cairo.Matrix.create_translate(1, 2) to draw a
+--        system. For example, use matrix.create_translate(1, 2) to draw a
 --        widget at position (1, 2) relative to the parent widget.
 -- @param width The width of the widget in its own coordinate system. That is,
 --        after applying the transformation matrix.
@@ -217,7 +216,7 @@ function base.place_widget_via_matrix(widget, mat, width, height)
         _widget = widget,
         _width = width,
         _height = height,
-        _matrix = matrix.copy(mat)
+        _matrix = mat
     }
 end
 
@@ -232,7 +231,7 @@ end
 --        after applying the transformation matrix.
 -- @return An opaque object that can be returned from :layout()
 function base.place_widget_at(widget, x, y, width, height)
-    return base.place_widget_via_matrix(widget, Matrix.create_translate(x, y), width, height)
+    return base.place_widget_via_matrix(widget, matrix.create_translate(x, y), width, height)
 end
 
 --[[--

spec/gears/matrix_spec.lua

@@ -7,48 +7,98 @@ local matrix = require("gears.matrix")
 local cairo = require("lgi").cairo
 
 describe("gears.matrix", function()
-    describe("copy", function()
+    local function round(n)
-        it("Test copy", function()
+        return math.floor(n + 0.5)
-            local m1 = cairo.Matrix()
+    end
-            m1:init(1, 2, 3, 4, 5, 6)
-            local m2 = matrix.copy(m1)
-            assert.is.equal(m1.xx, m2.xx)
-            assert.is.equal(m1.xy, m2.xy)
-            assert.is.equal(m1.yx, m2.yx)
-            assert.is.equal(m1.yy, m2.yy)
-            assert.is.equal(m1.x0, m2.x0)
-            assert.is.equal(m1.y0, m2.y0)
 
-            m1.x0 = 42
+    describe("cannot modify", function()
-            assert.is_not.equal(m1.x0, m2.x0)
+        assert.has.errors(function()
+            matrix.identity.something = 42
         end)
     end)
 
     describe("equals", function()
         it("Same matrix", function()
-            local m = cairo.Matrix.create_rotate(1)
+            local m = matrix.create_rotate(1)
             assert.is_true(matrix.equals(m, m))
+            assert.is.equal(m, m)
         end)
 
         it("Different matrix equals", function()
-            local m1 = cairo.Matrix.create_rotate(1)
+            local m1 = matrix.create_rotate(1)
-            local m2 = cairo.Matrix.create_rotate(1)
+            local m2 = matrix.create_rotate(1)
             assert.is_true(matrix.equals(m1, m2))
+            assert.is.equal(m1, m2)
         end)
 
         it("Different matrix unequal", function()
-            local m1 = cairo.Matrix()
+            local m1 = matrix.create(1, 2, 3, 4, 5, 6)
-            local m2 = cairo.Matrix()
+            local m2 = matrix.create(1, 2, 3, 4, 5, 0)
-            m1:init(1, 2, 3, 4, 5, 6)
-            m2:init(1, 2, 3, 4, 5, 0)
             assert.is_false(matrix.equals(m1, m2))
+            assert.is_not.equal(m1, m2)
+        end)
+
+        it("Identity matrix", function()
+            local m1 = matrix.identity
+            local m2 = matrix.create(1, 0, 0, 1, 0, 0)
+            assert.is_true(matrix.equals(m1, m2))
+            assert.is.equal(m1, m2)
+        end)
+    end)
+
+    describe("create", function()
+        it("translate", function()
+            assert.is.equal(matrix.create(1, 0, 0, 1, 2, 3), matrix.create_translate(2, 3))
+        end)
+
+        it("scale", function()
+            assert.is.equal(matrix.create(2, 0, 0, 3, 0, 0), matrix.create_scale(2, 3))
+        end)
+
+        it("rotate", function()
+            local m = matrix.create_rotate(math.pi / 2)
+            assert.is_true(math.abs(round(m.xx) - m.xx) < 0.00000001)
+            assert.is.equal(-1, m.xy)
+            assert.is.equal(1, m.yx)
+            assert.is_true(math.abs(round(m.yy) - m.yy) < 0.00000001)
+            assert.is.equal(0, m.x0)
+            assert.is.equal(0, m.y0)
+        end)
+    end)
+
+    it("multiply", function()
+        -- Just some random matrices which I multiplied by hand
+        local a = matrix.create(1, 2, 3, 4, 5, 6)
+        local b = matrix.create(7, 8, 9, 1, 1, 1)
+        local m = matrix.create(25, 10, 57, 28, 90, 47)
+        assert.is.equal(m, a:multiply(b))
+        assert.is.equal(m, a * b)
+    end)
+
+    describe("invert", function()
+        it("translate", function()
+            local m1, m2 = matrix.create_translate(2, 3), matrix.create_translate(-2, -3)
+            assert.is.equal(m2, m1:invert())
+            assert.is.equal(matrix.identity, m1 * m2)
+            assert.is.equal(matrix.identity, m2 * m1)
+        end)
+
+        it("scale", function()
+            local m1, m2 = matrix.create_scale(2, 3), matrix.create_scale(1/2, 1/3)
+            assert.is.equal(m2, m1:invert())
+            assert.is.equal(matrix.identity, m1 * m2)
+            assert.is.equal(matrix.identity, m2 * m1)
+        end)
+
+        it("rotate", function()
+            local m1, m2 = matrix.create_rotate(2), matrix.create_rotate(-2)
+            assert.is.equal(m2, m1:invert())
+            assert.is.equal(matrix.identity, m1 * m2)
+            assert.is.equal(matrix.identity, m2 * m1)
         end)
     end)
 
     describe("transform_rectangle", function()
-        local function round(n)
-            return math.floor(n + 0.5)
-        end
         local function test(m, x, y, width, height,
             expected_x, expected_y, expected_width, expected_height)
             local actual_x, actual_y, actual_width, actual_height =
@@ -64,19 +114,42 @@ describe("gears.matrix", function()
             assert.is_true(math.abs(round(actual_height) - actual_height) < 0.00000001)
         end
         it("Identity matrix", function()
-            test(cairo.Matrix.create_identity(), 1, 2, 3, 4, 1, 2, 3, 4)
+            test(matrix.identity, 1, 2, 3, 4, 1, 2, 3, 4)
         end)
 
         it("Rotate 180", function()
-            test(cairo.Matrix.create_rotate(math.pi),
+            test(matrix.create_rotate(math.pi),
                 1, 2, 3, 4, -4, -6, 3, 4)
         end)
 
         it("Rotate 90", function()
-            test(cairo.Matrix.create_rotate(math.pi / 2),
+            test(matrix.create_rotate(math.pi / 2),
                 1, 2, 3, 4, -6, 1, 4, 3)
         end)
     end)
+
+    it("tostring", function()
+        local m = matrix.create(1, 2, 3, 4, 5, 6)
+        local expected = "[[1, 2], [3, 4], [5, 6]]"
+        assert.is.equal(expected, m:tostring())
+        assert.is.equal(expected, tostring(m))
+    end)
+
+    it("from_cairo_matrix", function()
+        local m1 = matrix.create_translate(2, 3)
+        local m2 = matrix.from_cairo_matrix(cairo.Matrix.create_translate(2, 3))
+        assert.is.equal(m1, m2)
+    end)
+
+    it("to_cairo_matrix", function()
+        local m = matrix.create_scale(3, 4):to_cairo_matrix()
+        assert.is.equal(3, m.xx)
+        assert.is.equal(0, m.xy)
+        assert.is.equal(0, m.yx)
+        assert.is.equal(4, m.yy)
+        assert.is.equal(0, m.x0)
+        assert.is.equal(0, m.y0)
+    end)
 end)
 
 -- vim: filetype=lua:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:textwidth=80

spec/wibox/hierarchy_spec.lua

@@ -5,7 +5,7 @@
 
 local hierarchy = require("wibox.hierarchy")
 
-local cairo = require("lgi").cairo
+local Region = require("lgi").cairo.Region
 local matrix = require("gears.matrix")
 local object = require("gears.object")
 local utils = require("wibox.test_utils")
@@ -37,23 +37,19 @@ describe("wibox.hierarchy", function()
         end)
 
         it("get_matrix_to_parent", function()
-            assert.is_true(matrix.equals(cairo.Matrix.create_identity(),
+            assert.is.equal(matrix.identity, instance:get_matrix_to_parent())
-                    instance:get_matrix_to_parent()))
         end)
 
         it("get_matrix_to_device", function()
-            assert.is_true(matrix.equals(cairo.Matrix.create_identity(),
+            assert.is.equal(matrix.identity, instance:get_matrix_to_device())
-                    instance:get_matrix_to_device()))
         end)
 
         it("get_matrix_from_parent", function()
-            assert.is_true(matrix.equals(cairo.Matrix.create_identity(),
+            assert.is.equal(matrix.identity, instance:get_matrix_from_parent())
-                    instance:get_matrix_from_parent()))
         end)
 
         it("get_matrix_from_device", function()
-            assert.is_true(matrix.equals(cairo.Matrix.create_identity(),
+            assert.is.equal(matrix.identity, instance:get_matrix_from_device())
-                    instance:get_matrix_from_device()))
         end)
 
         it("get_draw_extents", function()
@@ -72,7 +68,7 @@ describe("wibox.hierarchy", function()
     it("disconnect works", function()
         local child = make_widget(nil)
         local parent = make_widget({
-            make_child(child, 2, 5, cairo.Matrix.create_translate(10, 0))
+            make_child(child, 2, 5, matrix.create_translate(10, 0))
         })
 
         local extra_arg = {}
@@ -129,10 +125,10 @@ describe("wibox.hierarchy", function()
         before_each(function()
             child = make_widget(nil)
             intermediate = make_widget({
-                make_child(child, 10, 20, cairo.Matrix.create_translate(0, 5))
+                make_child(child, 10, 20, matrix.create_translate(0, 5))
             })
             parent = make_widget({
-                make_child(intermediate, 5, 2, cairo.Matrix.create_translate(4, 0))
+                make_child(intermediate, 5, 2, matrix.create_translate(4, 0))
             })
 
             local function nop() end
@@ -156,27 +152,27 @@ describe("wibox.hierarchy", function()
         end)
 
         it("get_matrix_to_parent", function()
-            assert.is_true(matrix.equals(hierarchy_child:get_matrix_to_parent(), cairo.Matrix.create_translate(0, 5)))
+            assert.is.equal(hierarchy_child:get_matrix_to_parent(), matrix.create_translate(0, 5))
-            assert.is_true(matrix.equals(hierarchy_intermediate:get_matrix_to_parent(), cairo.Matrix.create_translate(4, 0)))
+            assert.is.equal(hierarchy_intermediate:get_matrix_to_parent(), matrix.create_translate(4, 0))
-            assert.is_true(matrix.equals(hierarchy_parent:get_matrix_to_parent(), cairo.Matrix.create_identity()))
+            assert.is.equal(hierarchy_parent:get_matrix_to_parent(), matrix.identity)
         end)
 
         it("get_matrix_to_device", function()
-            assert.is_true(matrix.equals(hierarchy_child:get_matrix_to_device(), cairo.Matrix.create_translate(4, 5)))
+            assert.is.equal(hierarchy_child:get_matrix_to_device(), matrix.create_translate(4, 5))
-            assert.is_true(matrix.equals(hierarchy_intermediate:get_matrix_to_device(), cairo.Matrix.create_translate(4, 0)))
+            assert.is.equal(hierarchy_intermediate:get_matrix_to_device(), matrix.create_translate(4, 0))
-            assert.is_true(matrix.equals(hierarchy_parent:get_matrix_to_device(), cairo.Matrix.create_identity()))
+            assert.is.equal(hierarchy_parent:get_matrix_to_device(), matrix.identity)
         end)
 
         it("get_matrix_from_parent", function()
-            assert.is_true(matrix.equals(hierarchy_child:get_matrix_from_parent(), cairo.Matrix.create_translate(0, -5)))
+            assert.is.equal(hierarchy_child:get_matrix_from_parent(), matrix.create_translate(0, -5))
-            assert.is_true(matrix.equals(hierarchy_intermediate:get_matrix_from_parent(), cairo.Matrix.create_translate(-4, 0)))
+            assert.is.equal(hierarchy_intermediate:get_matrix_from_parent(), matrix.create_translate(-4, 0))
-            assert.is_true(matrix.equals(hierarchy_parent:get_matrix_from_parent(), cairo.Matrix.create_identity()))
+            assert.is.equal(hierarchy_parent:get_matrix_from_parent(), matrix.identity)
         end)
 
         it("get_matrix_from_device", function()
-            assert.is_true(matrix.equals(hierarchy_child:get_matrix_from_device(), cairo.Matrix.create_translate(-4, -5)))
+            assert.is.equal(hierarchy_child:get_matrix_from_device(), matrix.create_translate(-4, -5))
-            assert.is_true(matrix.equals(hierarchy_intermediate:get_matrix_from_device(), cairo.Matrix.create_translate(-4, 0)))
+            assert.is.equal(hierarchy_intermediate:get_matrix_from_device(), matrix.create_translate(-4, 0))
-            assert.is_true(matrix.equals(hierarchy_parent:get_matrix_from_device(), cairo.Matrix.create_identity()))
+            assert.is.equal(hierarchy_parent:get_matrix_from_device(), matrix.identity)
         end)
 
         it("get_draw_extents", function()
@@ -199,10 +195,10 @@ describe("wibox.hierarchy", function()
         before_each(function()
             child = make_widget(nil)
             intermediate = make_widget({
-                make_child(child, 10, 20, cairo.Matrix.create_translate(0, 5))
+                make_child(child, 10, 20, matrix.create_translate(0, 5))
             })
             parent = make_widget({
-                make_child(intermediate, 5, 2, cairo.Matrix.create_translate(4, 0))
+                make_child(intermediate, 5, 2, matrix.create_translate(4, 0))
             })
 
             local context = {}
@@ -218,7 +214,7 @@ describe("wibox.hierarchy", function()
 
         it("child moved", function()
             intermediate.layout = function()
-                return { make_child(child, 10, 20, cairo.Matrix.create_translate(0, 4)) }
+                return { make_child(child, 10, 20, matrix.create_translate(0, 4)) }
             end
             local context = {}
             local instance2 = hierarchy.new(context, parent, 15, 16, nop, nop)