From 22d656903563f75678f3634964731ccf93355dfd Mon Sep 17 00:00:00 2001 From: ache Date: Mon, 13 Mar 2017 23:17:19 +0100 Subject: Init commit --- lib/gears/matrix.lua | 219 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 219 insertions(+) create mode 100644 lib/gears/matrix.lua (limited to 'lib/gears/matrix.lua') diff --git a/lib/gears/matrix.lua b/lib/gears/matrix.lua new file mode 100644 index 0000000..a6bc975 --- /dev/null +++ b/lib/gears/matrix.lua @@ -0,0 +1,219 @@ +--------------------------------------------------------------------------- +-- An implementation of matrices for describing and working with affine +-- transformations. +-- @author Uli Schlachter +-- @copyright 2015 Uli Schlachter +-- @classmod gears.matrix +--------------------------------------------------------------------------- + +local cairo = require("lgi").cairo +local matrix = {} + +-- Metatable for matrix instances. This is set up near the end of the file. +local matrix_mt = {} + +--- Create a new matrix instance +-- @tparam number xx The xx transformation part. +-- @tparam number yx The yx transformation part. +-- @tparam number xy The xy transformation part. +-- @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 + +--- Create a new translation matrix +-- @tparam number x The translation in x direction. +-- @tparam number y The translation in y direction. +-- @return A new matrix describing the given transformation. +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 + +--- Create a new rotation matrix rotating around a custom point +-- @tparam number x The horizontal rotation point +-- @tparam number y The vertical rotation point +-- @tparam number angle The angle of the rotation in radians. +-- @return A new matrix describing the given transformation. +function matrix.create_rotate_at(x, y, angle) + return matrix.create_translate( -x, -y ) + * matrix.create_rotate ( angle ) + * matrix.create_translate( x, y ) +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 + +--- Rotate a shape from a custom point +-- @tparam number x The horizontal rotation point +-- @tparam number y The vertical rotation point +-- @tparam number angle The angle (in radiant: -2*math.pi to 2*math.pi) +-- @return A transformation object +function matrix:rotate_at(x, y, angle) + return self * matrix.create_rotate_at(x, y, angle) +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) + local ret = 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) + + return ret +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 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 y coordinate of the transformed point. +function matrix:transform_point(x, y) + 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. +-- @tparam number x The x coordinate of the rectangle. +-- @tparam number y The y coordinate of the rectangle. +-- @tparam number width The width of the rectangle. +-- @tparam number height The height of the rectangle. +-- @treturn number X coordinate of the bounding rectangle. +-- @treturn number Y coordinate of the bounding rectangle. +-- @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 = self:transform_point(x, y) + local x2, y2 = self:transform_point(x, y + height) + local x3, y3 = self:transform_point(x + width, y + height) + local x4, y4 = self:transform_point(x + width, y) + -- Find the extremal points of the result + x = math.min(x1, x2, x3, x4) + y = math.min(y1, y2, y3, y4) + width = math.max(x1, x2, x3, x4) - x + height = math.max(y1, y2, y3, y4) - y + + 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 -- cgit v1.2.3-54-g00ecf