Selector's toolbar: changing the dimensions of the visual bounding box of selection of multiple objects having different stroke widths has been fixed (bug #212768, #190557, ...)

Fixed bugs:
  - https://launchpad.net/bugs/212768
  - https://launchpad.net/bugs/190557

(bzr r10437.1.5)

1 files changed, 231 insertions, 42 deletions

diff --git a/src/sp-item-transform.cpp b/src/sp-item-transform.cpp
index ae55a5c50..45d965e44 100644
--- a/src/sp-item-transform.cpp
+++ b/src/sp-item-transform.cpp
@@ -7,8 +7,9 @@
  *   bulia byak <buliabyak@gmail.com>
  *   Johan Engelen <goejendaagh@zonnet.nl>
  *   Abhishek Sharma
+ *   Diederik van Lierop <mail@diedenrezi.nl>
  *
- * Copyright (C) 1999-2008 authors
+ * Copyright (C) 1999-2011 authors
  *
  * Released under GNU GPL, read the file 'COPYING' for more information
  */
@@ -67,46 +68,76 @@ sp_item_skew_rel (SPItem *item, double skewX, double skewY)
 
 void sp_item_move_rel(SPItem *item, Geom::Translate const &tr)
 {
-	item->set_i2d_affine(item->i2d_affine() * tr);
+    item->set_i2d_affine(item->i2d_affine() * tr);
 
-	item->doWriteTransform(item->getRepr(), item->transform);
+    item->doWriteTransform(item->getRepr(), item->transform);
 }
 
-/*
-** Returns the matrix you need to apply to an object with given visual bbox and strokewidth to
-scale/move it to the new visual bbox x0/y0/x1/y1. Takes into account the "scale stroke"
-preference value passed to it. Has to solve a quadratic equation to make sure
-the goal is met exactly and the stroke scaling is obeyed.
+/**
+ * \brief Calculate the affine transformation required to transform one visual bounding box into another, accounting for a uniform strokewidth
+ *
+ * PS: This function will only return accurate results for the visual bounding box of a selection of one of more objects, all having
+ * the same strokewidth. If the stroke width varies from object to object in this selection, then the function
+ * get_scale_transform_with_unequal_stroke() should be called instead
+ *
+ * When scaling or stretching an object using the selector, e.g. by dragging the handles or by entering a value, we will
+ * need to calculate the affine transformation for the old dimensions to the new dimensions. When using a geometric bounding
+ * box this is very straightforward, but when using a visual bounding box this become more tricky as we need to account for
+ * the strokewidth, which is either constant or scales width the area of the object. This function takes care of the calculation
+ * of the affine transformation:
+ * \param bbox_visual Current visual bounding box
+ * \param strokewidth Strokewidth
+ * \param transform_stroke If true then the stroke will be scaled proportional to the square root of the area of the geometric bounding box
+ * \param x0 Coordinate of the target visual bounding box
+ * \param y0 Coordinate of the target visual bounding box
+ * \param x1 Coordinate of the target visual bounding box
+ * \param y1 Coordinate of the target visual bounding box
+ *   PS: we have to pass each coordinate individually, to find out if we are mirroring the object; Using a Geom::Rect() instead is
+     not possible here because it will only allow for a positive width and height, and therefore cannot mirror
+ * \return
 */
 
 Geom::Affine
-get_scale_transform_with_stroke (Geom::Rect const &bbox_param, gdouble strokewidth, bool transform_stroke, gdouble x0, gdouble y0, gdouble x1, gdouble y1)
+get_scale_transform_with_uniform_stroke (Geom::Rect const &bbox_visual, gdouble strokewidth, bool transform_stroke, gdouble x0, gdouble y0, gdouble x1, gdouble y1)
 {
-    Geom::Rect bbox (bbox_param);
-
-    Geom::Affine p2o = Geom::Translate (-bbox.min());
+    Geom::Affine p2o = Geom::Translate (-bbox_visual.min());
     Geom::Affine o2n = Geom::Translate (x0, y0);
 
-    Geom::Affine scale = Geom::Scale (1, 1); // scale component
-    Geom::Affine unbudge = Geom::Translate (0, 0); // move component to compensate for the drift caused by stroke width change
+    Geom::Affine scale = Geom::Scale (1, 1);
+    Geom::Affine unbudge = Geom::Translate (0, 0); // moves the object(s) to compensate for the drift caused by stroke width change
+
+    // 1) We start with a visual bounding box (w0, h0) which we want to transfer into another visual bounding box (w1, h1)
+    // 2) The stroke is r0, equal for all edges
+    // 3) Given this visual bounding box we can calculate the geometric bounding box by subtracting half the stroke from each side;
+    // -> The width and height of the geometric bounding box will therefore be (w0 - 2*0.5*r0) and (h0 - 2*0.5*r0)
 
-    gdouble w0 = bbox[Geom::X].extent(); // will return a value >= 0, as required further down the road
-    gdouble h0 = bbox[Geom::Y].extent();
+    gdouble w0 = bbox_visual.width(); // will return a value >= 0, as required further down the road
+    gdouble h0 = bbox_visual.height();
+    gdouble r0 = fabs(strokewidth);
+
+    // We also know the width and height of the new visual bounding box
     gdouble w1 = x1 - x0; // can have any sign
     gdouble h1 = y1 - y0;
-    gdouble r0 = strokewidth;
+    // The new visual bounding box will have a stroke r1
+
+    // We will now try to calculate the affine transformation required to transform the first visual bounding box into
+    // the second one, while accounting for strokewidth
 
-    if (bbox.hasZeroArea()) {
-        Geom::Affine move = Geom::Translate(x0 - bbox.min()[Geom::X], y0 - bbox.min()[Geom::Y]);
-        return (move); // cannot scale from empty boxes at all, so only translate
+    if (bbox_visual.hasZeroArea()) { // Obviously we cannot scale from empty visual bounding boxes at all, so we will only translate in such a case
+        Geom::Affine move = Geom::Translate(x0 - bbox_visual.min()[Geom::X], y0 - bbox_visual.min()[Geom::Y]);
+        return (move);
     }
 
-    Geom::Affine direct = Geom::Scale(w1 / w0,   h1 / h0);
+    Geom::Affine direct = Geom::Scale(w1 / w0,   h1 / h0); // Scaling of the visual bounding box
 
+    // Although the area of the visual bounding box is not zero, we can still have a geometric
+    // bounding box with one or both sides having zero length. We can't handle this and will therefore
+    // simply return the scaling of the visual bounding box, without accounting for any stroke scaling
     if (fabs(w0 - r0) < 1e-6 || fabs(h0 - r0) < 1e-6 || (!transform_stroke && (fabs(w1 - r0) < 1e-6 || fabs(h1 - r0) < 1e-6))) {
-        return (p2o * direct * o2n); // can't solve the equation: one of the dimensions is equal to stroke width, so return the straightforward scaler
+        return (p2o * direct * o2n);
     }
 
+    // Here starts the calculation you've been waiting for; first do some preparation
     int flip_x = (w1 > 0) ? 1 : -1;
     int flip_y = (h1 > 0) ? 1 : -1;
     
@@ -115,43 +146,201 @@ get_scale_transform_with_stroke (Geom::Rect const &bbox_param, gdouble strokewid
     w1 = fabs(w1);
     h1 = fabs(h1);
     r0 = fabs(r0);
-    // w0 and h0 will always be positive due to the definition extent()
+    // w0 and h0 will always be positive due to the definition of the width() and height() methods.
 
-    gdouble ratio_x = (w1 - r0) / (w0 - r0);
+    gdouble ratio_x = (w1 - r0) / (w0 - r0); // Only valid when the stroke is kept constant, in which case r1 = r0
     gdouble ratio_y = (h1 - r0) / (h0 - r0);
-    
+
+    // Calculating the scaling of the geometric bounding box if the stroke is kept constant
     Geom::Affine direct_constant_r = Geom::Scale(flip_x * ratio_x, flip_y * ratio_y);
 
-    if (transform_stroke && r0 != 0 && r0 != Geom::infinity()) { // there's stroke, and we need to scale it
-        // These coefficients are obtained from the assumption that scaling applies to the
-        // non-stroked "shape proper" and that stroke scale is scaled by the expansion of that
-        // matrix. We're trying to solve this equation:
-        // r1 = r0 * sqrt (((w1-r0)/(w0-r0))*((h1-r0)/(h0-r0)))
-        // The operant of the sqrt() must be positive, which is ensured by the fabs() a few lines above
+    // If the stroke is not kept constant however, the scaling of the geometric bbox is more difficult to find
+    if (transform_stroke && r0 != 0 && r0 != Geom::infinity()) { // Check if there's stroke, and we need to scale it
+        /* Initial area of the geometric bounding box: A0 = (w0-r0)*(h0-r0)
+         * Desired area of the geometric bounding box: A1 = (w1-r1)*(h1-r1)
+         * This is how the stroke should scale: r1^2 / A1 = r0^2 / A0
+         * So therefore we will need to solve this equation:
+         *
+         * r1^2 * (w0-r0) * (h1-r1) = r0^2 * (w1-r1) * (h0-r0)
+         *
+         * This is a quadratic equation in r1, of which the roots can be found using the ABC formula
+         * */
         gdouble A = -w0*h0 + r0*(w0 + h0);
         gdouble B = -(w1 + h1) * r0*r0;
         gdouble C = w1 * h1 * r0*r0;
         if (B*B - 4*A*C > 0) {
+            // Of the two roots, I verified experimentally that this is the one we need
             gdouble r1 = fabs((-B - sqrt(B*B - 4*A*C))/(2*A));
-            //gdouble r2 = (-B + sqrt (B*B - 4*A*C))/(2*A);
-            //std::cout << "r0" << r0 << " r1" << r1 << " r2" << r2 << "\n";
-            //
-            // If w1 < 0 then the scale will be wrong if we just do
-            // gdouble scale_x = (w1 - r1)/(w0 - r0);
-            // Here we also need the absolute values of w0, w1, h0, h1, and r1
+            // If w1 < 0 then the scale will be wrong if we just assume that scale_x = (w1 - r1)/(w0 - r0);
+            // Therefore we here need the absolute values of w0, w1, h0, h1, and r0, as taken care of earlier
             gdouble scale_x = (w1 - r1)/(w0 - r0);
             gdouble scale_y = (h1 - r1)/(h0 - r0);
+            // Now we account for mirroring by flipping if needed
             scale *= Geom::Scale(flip_x * scale_x, flip_y * scale_y);
+            // Make sure that the lower-left corner of the visual bounding box stays where it is, even though the stroke width has changed
             unbudge *= Geom::Translate (-flip_x * 0.5 * (r0 * scale_x - r1), -flip_y * 0.5 * (r0 * scale_y - r1));
-        } else {
+        } else { // Can't find the roots of the quadratic equation. Likely the input parameters are invalid?
             scale *= direct;
         }
-    } else {
-        if (r0 == 0 || r0 == Geom::infinity()) { // no stroke to scale
-            scale *= direct;
-        } else {// nonscaling strokewidth
+    } else { // The stroke should not be scaled, or is zero
+        if (!transform_stroke) { // Nonscaling strokewidth
             scale *= direct_constant_r;
             unbudge *= Geom::Translate (flip_x * 0.5 * r0 * (1 - ratio_x), flip_y * 0.5 * r0 * (1 - ratio_y));
+        } else { // Strokewidth is zero or infinite
+            scale *= direct;
+        }
+    }
+
+    return (p2o * scale * unbudge * o2n);
+}
+
+/**
+ * \brief Calculate the affine transformation required to transform one visual bounding box into another, accounting for a VARIABLE strokewidth
+ *
+ * Note: Please try to understand get_scale_transform_with_uniform_stroke() first, and read all it's comments carefully. This function
+ * (get_scale_transform_with_unequal_stroke) is a bit different because it will allow for a strokewidth that's different for each
+ * side of the visual bounding box. Such a situation will arise when transforming the visual bounding box of a selection of objects,
+ * each having a different stroke width. In fact this function is a generalized version of get_scale_transform_with_uniform_stroke(), but
+ * will not (yet) replace it because it has not been tested as carefully, and because the old function is can serve as an introduction to
+ * understand the new one.
+ *
+ * When scaling or stretching an object using the selector, e.g. by dragging the handles or by entering a value, we will
+ * need to calculate the affine transformation for the old dimensions to the new dimensions. When using a geometric bounding
+ * box this is very straightforward, but when using a visual bounding box this become more tricky as we need to account for
+ * the strokewidth, which is either constant or scales width the area of the object. This function takes care of the calculation
+ * of the affine transformation:
+ *
+ * \param bbox_visual Current visual bounding box
+ * \param bbox_geometric Current geometric bounding box (allows for calculating the strokewidth of each edge)
+ * \param transform_stroke If true then the stroke will be scaled proportional to the square root of the area of the geometric bounding box
+ * \param x0 Coordinate of the target visual bounding box
+ * \param y0 Coordinate of the target visual bounding box
+ * \param x1 Coordinate of the target visual bounding box
+ * \param y1 Coordinate of the target visual bounding box
+     PS: we have to pass each coordinate individually, to find out if we are mirroring the object; Using a Geom::Rect() instead is
+     not possible here because it will only allow for a positive width and height, and therefore cannot mirror
+ * \return
+*/
+
+Geom::Affine
+get_scale_transform_with_unequal_stroke (Geom::Rect const &bbox_visual, Geom::Rect const &bbox_geom, bool transform_stroke, gdouble x0, gdouble y0, gdouble x1, gdouble y1)
+{
+    Geom::Affine p2o = Geom::Translate (-bbox_visual.min());
+    Geom::Affine o2n = Geom::Translate (x0, y0);
+
+    Geom::Affine scale = Geom::Scale (1, 1);
+    Geom::Affine unbudge = Geom::Translate (0, 0);  // moves the object(s) to compensate for the drift caused by stroke width change
+
+    // 1) We start with a visual bounding box (w0, h0) which we want to transfer into another visual bounding box (w1, h1)
+    // 2) We will also know the geometric bounding box, which can be used to calculate the strokewidth. The strokewidth will however
+    //      be different for each of the four sides (left/right/top/bottom: r0l, r0r, r0t, r0b)
+
+    gdouble w0 = bbox_visual.width(); // will return a value >= 0, as required further down the road
+    gdouble h0 = bbox_visual.height();
+
+    // We also know the width and height of the new visual bounding box
+    gdouble w1 = x1 - x0; // can have any sign
+    gdouble h1 = y1 - y0;
+    // The new visual bounding box will have strokes r1l, r1r, r1t, and r1b
+
+    // We will now try to calculate the affine transformation required to transform the first visual bounding box into
+    // the second one, while accounting for strokewidth
+    gdouble r0w = w0 - bbox_geom.width(); // r0w is the average strokewidth of the left and right edges, i.e. 0.5*(r0l + r0r)
+    gdouble r0h = h0 - bbox_geom.height(); // r0h is the average strokewidth of the top and bottom edges, i.e. 0.5*(r0t + r0b)
+
+    // Check whether the stroke is not negative; should not be possible, but just in case:
+    g_assert(r0w >= 0);
+    g_assert(r0h >= 0);
+
+    if (bbox_visual.hasZeroArea()) { // Obviously we cannot scale from empty visual bounding boxes at all, so we will only translate in such a case
+        Geom::Affine move = Geom::Translate(x0 - bbox_visual.min()[Geom::X], y0 - bbox_visual.min()[Geom::Y]);
+        return (move);
+    }
+
+    Geom::Affine direct = Geom::Scale(w1 / w0,   h1 / h0);
+
+    // Although the area of the visual bounding box is not zero, we can still have a geometric
+    // bounding box with one or both sides having zero length. We can't handle this and will therefore
+    // simply return the scaling of the visual bounding box, without accounting for any stroke scaling
+    if (fabs(w0 - r0w) < 1e-6 || fabs(h0 - r0h) < 1e-6 || (!transform_stroke && (fabs(w1 - r0w) < 1e-6 || fabs(h1 - r0h) < 1e-6))) {
+        return (p2o * direct * o2n);
+    }
+
+    // Here starts the calculation you've been waiting for; first do some preparation
+    int flip_x = (w1 > 0) ? 1 : -1;
+    int flip_y = (h1 > 0) ? 1 : -1;
+
+    // w1 and h1 will be negative when mirroring, but if so then e.g. w1-r0 won't make sense
+    // Therefore we will use the absolute values from this point on
+    w1 = fabs(w1);
+    h1 = fabs(h1);
+    // w0 and h0 will always be positive due to the definition of the width() and height() methods.
+
+    gdouble ratio_x = (w1 - r0w) / (w0 - r0w); // Only valid when the stroke is kept constant, in which case r1 = r0
+    gdouble ratio_y = (h1 - r0h) / (h0 - r0h);
+
+    // Calculating the scaling of the geometric bounding box if the stroke is kept constant
+    Geom::Affine direct_constant_r = Geom::Scale(flip_x * ratio_x, flip_y * ratio_y);
+
+    // The calculation of the new strokewidth will only use the average stroke for each of the dimensions; To find the new stroke for each
+    // of the edges individually though, we will use the boundary condition that the ratio of the left/right strokewidth will not change due to the
+    // scaling. The same holds for the ratio of the top/bottom strokewidth.
+    gdouble stroke_ratio_w = fabs(r0w) < 1e-6 ? 1 : (bbox_geom[Geom::X].min() - bbox_visual[Geom::X].min())/r0w;
+    gdouble stroke_ratio_h = fabs(r0h) < 1e-6 ? 1 : (bbox_geom[Geom::Y].min() - bbox_visual[Geom::Y].min())/r0h;
+
+    // If the stroke is not kept constant however, the scaling of the geometric bbox is more difficult to find
+    if (transform_stroke && r0w != 0 && r0w != Geom::infinity() && r0h != 0 && r0h != Geom::infinity()) {  // Check if there's stroke, and we need to scale it
+        /* Initial area of the geometric bounding box: A0 = (w0-r0w)*(h0-r0h)
+         * Desired area of the geometric bounding box: A1 = (w1-r1w)*(h1-r1h)
+         * This is how the stroke should scale:     r1w^2 = A1/A0 * r0w^2, AND
+         *                                          r1h^2 = A1/A0 * r0h^2
+         * Now we have to solve this set of two equations and find r1w and r1h; this too complicated to do by hand,
+         * so I used wxMaxima for that (http://wxmaxima.sourceforge.net/). These lines can be copied into Maxima
+         *
+         * A1: (w1-r1w)*(h1-r1h);
+         * s: A1/A0;
+         * expr1a: r1w^2 = s*r0w^2;
+         * expr1b: r1h^2 = s*r0h^2;
+         * sol: solve([expr1a, expr1b], [r1h, r1w]);
+         * sol[1][1]; sol[2][1]; sol[3][1]; sol[4][1];
+         * sol[1][2]; sol[2][2]; sol[3][2]; sol[4][2];
+         *
+         * PS1: The last two lines are only needed for readability of the output, and can be omitted if desired
+         * PS2: A0 is known beforehand and assumed to be constant, instead of using A0 = (w0-r0w)*(h0-r0h). This reduces the
+         * length of the results significantly
+         * PS3: You'll get 8 solutions, 4 for each of the strokewidths r1w and r1h. Some experiments quickly showed which of the solutions
+         * lead to meaningful strokewidths
+         * */
+        gdouble r0h2 = r0h*r0h;
+        gdouble r0h3 = r0h2*r0h;
+        gdouble r0w2 = r0w*r0w;
+        gdouble w12 = w1*w1;
+        gdouble h12 = h1*h1;
+        gdouble A0 = bbox_geom.area();
+        gdouble A02 = A0*A0;
+
+        gdouble operant = 4*h1*w1*A0+r0h2*w12-2*h1*r0h*r0w*w1+h12*r0w2;
+        if (operant >= 0) {
+            // Of the eight roots, I verified experimentally that these are the two we need
+            gdouble r1h= fabs((r0h*sqrt(operant)-r0h2*w1-h1*r0h*r0w)/(2*A0-2*r0h*r0w));
+            gdouble r1w= fabs(-((h1*r0w*A0+r0h2*r0w*w1)*sqrt(operant)+(-3*h1*r0h*r0w*w1-h12*r0w2)*A0-r0h3*r0w*w12+h1*r0h2*r0w2*w1)/((r0h*A0-r0h2*r0w)*sqrt(operant)-2*h1*A02+(3*h1*r0h*r0w-r0h2*w1)*A0+r0h3*r0w*w1-h1*r0h2*r0w2));
+            // If w1 < 0 then the scale will be wrong if we just assume that scale_x = (w1 - r1)/(w0 - r0);
+            // Therefore we here need the absolute values of w0, w1, h0, h1, and r0, as taken care of earlier
+            gdouble scale_x = (w1 - r1w)/(w0 - r0w);
+            gdouble scale_y = (h1 - r1h)/(h0 - r0h);
+            // Now we account for mirroring by flipping if needed
+            scale *= Geom::Scale(flip_x * scale_x, flip_y * scale_y);
+            // Make sure that the lower-left corner of the visual bounding box stays where it is, even though the stroke width has changed
+            unbudge *= Geom::Translate (-flip_x * stroke_ratio_w * (r0w * scale_x - r1w), -flip_y * stroke_ratio_h * (r0h * scale_y - r1h));
+        } else { // Can't find the roots of the quadratic equation. Likely the input parameters are invalid?
+            scale *= direct;
+        }
+    } else { // The stroke should not be scaled, or is zero (or infinite)
+        if (!transform_stroke) {
+            scale *= direct_constant_r;
+            unbudge *= Geom::Translate (flip_x * stroke_ratio_w * r0w * (1 - ratio_x), flip_y * stroke_ratio_h * r0h * (1 - ratio_y));
+        } else { // can't calculate, because apparently strokewidth is zero or infinite
+            scale *= direct;
         }
     }