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+-- Copyright 2012 by Till Tantau
+--
+-- This file may be distributed an/or modified
+--
+-- 1. under the LaTeX Project Public License and/or
+-- 2. under the GNU Public License
+--
+-- See the file doc/generic/pgf/licenses/LICENSE for more information
+
+-- @release $Header: /cvsroot/pgf/pgf/generic/pgf/graphdrawing/lua/pgf/gd/lib/Transform.lua,v 1.1 2012/11/27 17:24:26 tantau Exp $
+
+
+---
+-- The |Transform| table provides a set of static methods for
+-- creating and handling canvas transformation matrices. Such a matrix
+-- is actually just an array of six numbers. The idea is that
+-- ``applying'' an array { a, b, c, d, e, f } a vector $(x,y)$ will
+-- yield the new vector $(ax+by+e,cx+dy+f)$. For details on how such
+-- matrices work, see Section~\ref{section-transform-cm}
+--
+local Transform = {}
+
+
+-- Namespace
+
+require("pgf.gd.model").Transform = Transform
+
+
+--- Creates a new transformation array.
+--
+-- @param a First component
+-- @param b Second component
+-- @param c Third component
+-- @param d Fourth component
+-- @param x The x shift
+-- @param y The y shift
+--
+-- @return A transformation object.
+--
+function Transform.new(a,b,c,d,x,y)
+ return { a, b, c, d, x, y }
+end
+
+
+--- Creates a new transformation object that represents a shift.
+--
+-- @param x An x-shift
+-- @param y A y-shift
+--
+-- @return A transformation object
+--
+function Transform.new_shift(x,y)
+ return { 1, 0, 0, 1, x, y }
+end
+
+
+--- Creates a new transformation object that represents a rotation.
+--
+-- @param angle An angle
+--
+-- @return A transformation object
+--
+function Transform.new_rotation(angle)
+ local c = math.cos(angle)
+ local s = math.sin(angle)
+ return { c, -s, s, c, 0, 0 }
+end
+
+
+--- Creates a new transformation object that represents a scaling.
+--
+-- @param x The horizontal scaling
+-- @param y The vertical scaling (if missing, the horizontal scaling is used)
+--
+-- @return A transformation object
+--
+function Transform.new_scaling(x_scale, y_scale)
+ return { x_scale, 0, 0, y_scale or x_scale, 0, 0 }
+end
+
+
+
+
+---
+-- Concatenate two transformation matrices, returning the new one.
+--
+-- @param a The first transformation
+-- @param b The second transformation
+--
+-- @return The transformation representing first applying |b| and then
+-- applying |a|.
+--
+function Transform.concat(a,b)
+ local a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6 =
+ a[1], a[2], a[3], a[4], a[5], a[6], b[1], b[2], b[3], b[4], b[5], b[6]
+ return { a1*b1 + a2*b3, a1*b2 + a2*b4,
+ a3*b1 + a4*b3, a3*b2 + a4*b4,
+ a1*b5 + a2*b6 + a5, a3*b5 + a4*b6 + a6 }
+end
+
+
+-- Done
+
+return Transform \ No newline at end of file