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+// SPDX-License-Identifier: GPL-2.0-or-later
+/*
+ * Transforming single items
+ *
+ * Authors:
+ * Lauris Kaplinski <lauris@kaplinski.com>
+ * Frank Felfe <innerspace@iname.com>
+ * bulia byak <buliabyak@gmail.com>
+ * Johan Engelen <goejendaagh@zonnet.nl>
+ * Abhishek Sharma
+ * Diederik van Lierop <mail@diedenrezi.nl>
+ *
+ * Copyright (C) 1999-2011 authors
+ *
+ * Released under GNU GPL v2+, read the file 'COPYING' for more information.
+ */
+
+#include <2geom/transforms.h>
+#include "sp-item.h"
+#include "sp-item-transform.h"
+
+#include <glib.h>
+
+/**
+ * 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 or 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_for_variable_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 stroke_x Apparent strokewidth in horizontal direction
+ * @param stroke_y Apparent strokewidth in vertical direction
+ * @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 preserve If true then the transform element will be preserved in XML, and evaluated after stroke is applied
+ * @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_for_uniform_stroke(Geom::Rect const &bbox_visual, gdouble stroke_x, gdouble stroke_y, bool transform_stroke, bool preserve, 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) The stroke is r0, equal for all edges, if preserve transforms is false
+ // 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)
+ // 4) If preserve transforms is true, then stroke_x != stroke_y, since these are the apparent stroke widths, after transforming
+
+ if ((stroke_x == Geom::infinity()) || (fabs(stroke_x) < 1e-6)) stroke_x = 0;
+ if ((stroke_y == Geom::infinity()) || (fabs(stroke_y) < 1e-6)) stroke_y = 0;
+
+ 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 a stroke r1
+
+ // 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.
+
+ // Check whether the stroke is negative; i.e. the geometric bounding box is larger than the visual bounding box, which
+ // occurs for example for clipped objects (see launchpad bug #811819)
+ if (stroke_x < 0 || stroke_y < 0) {
+ Geom::Affine direct = Geom::Scale(flip_x * w1 / w0, flip_y* h1 / h0); // Scaling of the visual bounding box
+ // How should we handle the stroke width scaling of clipped object? I don't know if we can/should handle this,
+ // so for now we simply return the direct scaling
+ return (p2o * direct * o2n);
+ }
+ gdouble r0 = sqrt(stroke_x*stroke_y); // r0 is redundant, used only for those cases where stroke_x = stroke_y
+
+ // 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 ((fabs(w0 - stroke_x) < 1e-6) && (fabs(h0 - stroke_y) < 1e-6)) {
+ return Geom::Affine();
+ }
+
+ gdouble scale_x = 1;
+ gdouble scale_y = 1;
+ gdouble r1;
+
+ if ((fabs(w0 - stroke_x) < 1e-6) || w1 == 0) { // We have a vertical line at hand
+ scale_y = h1/h0;
+ scale_x = transform_stroke ? 1 : scale_y;
+ unbudge *= Geom::Translate (-flip_x * 0.5 * (scale_x - 1.0) * w0, 0);
+ unbudge *= Geom::Translate ( flip_x * 0.5 * (w1 - w0), 0); // compensate for the fact that this operation cannot be performed
+ } else if ((fabs(h0 - stroke_y) < 1e-6) || h1 == 0) { // We have a horizontal line at hand
+ scale_x = w1/w0;
+ scale_y = transform_stroke ? 1 : scale_x;
+ unbudge *= Geom::Translate (0, -flip_y * 0.5 * (scale_y - 1.0) * h0);
+ unbudge *= Geom::Translate (0, flip_y * 0.5 * (h1 - h0)); // compensate for the fact that this operation cannot be performed
+ } else { // We have a true 2D object at hand
+ if (transform_stroke && !preserve) {
+ /* 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) * (h0-r0) = r0^2 * (w1-r1) * (h1-r1)
+ *
+ * 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) {
+ g_message("stroke scaling error : %d, %f, %f, %f, %f, %f", preserve, r0, w0, h0, w1, h1);
+ } else {
+ r1 = -C/B;
+ if (!Geom::are_near(A*C/B/B, 0.0, Geom::EPSILON))
+ r1 = fabs((-B - sqrt(B*B - 4*A*C))/(2*A));
+ // 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
+ scale_x = (w1 - r1)/(w0 - r0);
+ scale_y = (h1 - r1)/(h0 - r0);
+ // 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 if (!transform_stroke && !preserve) { // scale the geometric bbox with constant stroke
+ scale_x = (w1 - r0) / (w0 - r0);
+ scale_y = (h1 - r0) / (h0 - r0);
+ unbudge *= Geom::Translate (-flip_x * 0.5 * r0 * (scale_x - 1), -flip_y * 0.5 * r0 * (scale_y - 1));
+ } else if (!transform_stroke) { // 'Preserve Transforms' was chosen.
+ // geometric mean of stroke_x and stroke_y will be preserved
+ // new_stroke_x = stroke_x*sqrt(scale_x/scale_y)
+ // new_stroke_y = stroke_y*sqrt(scale_y/scale_x)
+ // scale_x = (w1 - new_stroke_x)/(w0 - stroke_x)
+ // scale_y = (h1 - new_stroke_y)/(h0 - stroke_y)
+ gdouble A = h1*(w0 - stroke_x);
+ gdouble B = (h0*stroke_x - w0*stroke_y);
+ gdouble C = -w1*(h0 - stroke_y);
+ gdouble Sx_div_Sy; // Sx_div_Sy = sqrt(scale_x/scale_y)
+ if (B*B - 4*A*C < 0) {
+ g_message("stroke scaling error : %d, %f, %f, %f, %f, %f, %f", preserve, stroke_x, stroke_y, w0, h0, w1, h1);
+ } else {
+ Sx_div_Sy = (-B + sqrt(B*B - 4*A*C))/2/A;
+ scale_x = (w1 - stroke_x*Sx_div_Sy)/(w0 - stroke_x);
+ scale_y = (h1 - stroke_y/Sx_div_Sy)/(h0 - stroke_y);
+ unbudge *= Geom::Translate (-flip_x * 0.5 * stroke_x * scale_x * (1.0 - sqrt(1.0/scale_x/scale_y)), -flip_y * 0.5 * stroke_y * scale_y * (1.0 - sqrt(1.0/scale_x/scale_y)));
+ }
+ } else { // 'Preserve Transforms' was chosen, and stroke is scaled
+ scale_x = w1 / w0;
+ scale_y = h1 / h0;
+ }
+ }
+
+ // Now we account for mirroring by flipping if needed
+ scale *= Geom::Scale(flip_x * scale_x, flip_y * scale_y);
+
+ return (p2o * scale * unbudge * o2n);
+}
+
+/**
+ * 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_for_uniform_stroke() first, and read all it's comments carefully. This function
+ * (get_scale_transform_for_variable_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_for_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 preserve If true then the transform element will be preserved in XML, and evaluated after stroke is applied
+ * @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_for_variable_stroke(Geom::Rect const &bbox_visual, Geom::Rect const &bbox_geom, bool transform_stroke, bool preserve, 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)
+ if ((r0w == Geom::infinity()) || (fabs(r0w) < 1e-6)) r0w = 0;
+ if ((r0h == Geom::infinity()) || (fabs(r0h) < 1e-6)) r0h = 0;
+
+ 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.
+
+ if ((fabs(w0 - r0w) < 1e-6) && (fabs(h0 - r0h) < 1e-6)) {
+ return Geom::Affine();
+ }
+
+ // Check whether the stroke is negative; i.e. the geometric bounding box is larger than the visual bounding box, which
+ // occurs for example for clipped objects (see launchpad bug #811819)
+ if (r0w < 0 || r0h < 0) {
+ Geom::Affine direct = Geom::Scale(flip_x * w1 / w0, flip_y* h1 / h0); // Scaling of the visual bounding box
+ // How should we handle the stroke width scaling of clipped object? I don't know if we can/should handle this,
+ // so for now we simply return the direct scaling
+ return (p2o * direct * o2n);
+ }
+
+ // 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;
+
+ gdouble scale_x = 1;
+ gdouble scale_y = 1;
+ gdouble r1h;
+ gdouble r1w;
+
+ if ((fabs(w0 - r0w) < 1e-6) || w1 == 0) { // We have a vertical line at hand
+ scale_y = h1/h0;
+ scale_x = transform_stroke ? 1 : scale_y;
+ unbudge *= Geom::Translate (-flip_x * 0.5 * (scale_x - 1.0) * w0, 0);
+ unbudge *= Geom::Translate ( flip_x * 0.5 * (w1 - w0), 0); // compensate for the fact that this operation cannot be performed
+ } else if ((fabs(h0 - r0h) < 1e-6) || h1 == 0) { // We have a horizontal line at hand
+ scale_x = w1/w0;
+ scale_y = transform_stroke ? 1 : scale_x;
+ unbudge *= Geom::Translate (0, -flip_y * 0.5 * (scale_y - 1.0) * h0);
+ unbudge *= Geom::Translate (0, flip_y * 0.5 * (h1 - h0)); // compensate for the fact that this operation cannot be performed
+ } else { // We have a true 2D object at hand
+ if (transform_stroke && !preserve) {
+ /* 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
+ * These can be re-expressed as : r1w/r0w = r1h/r0h
+ * and : r1w*r1w*(w0 - r0w)*(h0 - r0h) = r0w*r0w*(w1 - r1w)*(h1 - r1h)
+ * This leads to a quadratic equation in r1w, solved as follows:
+ * */
+
+ gdouble A = w0*h0 - r0h*w0 - r0w*h0;
+ gdouble B = r0h*w1 + r0w*h1;
+ gdouble C = -w1*h1;
+
+ if (B*B - 4*A*C < 0) {
+ g_message("variable stroke scaling error : %d, %d, %f, %f, %f, %f, %f, %f", transform_stroke, preserve, r0w, r0h, w0, h0, w1, h1);
+ } else {
+ gdouble det = -C/B;
+ if (!Geom::are_near(A*C/B/B, 0.0, Geom::EPSILON))
+ det = (-B + sqrt(B*B - 4*A*C))/(2*A);
+ r1w = r0w*det;
+ r1h = r0h*det;
+ // 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
+ scale_x = (w1 - r1w)/(w0 - r0w);
+ scale_y = (h1 - r1h)/(h0 - r0h);
+ // 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 if (!transform_stroke && !preserve) { // scale the geometric bbox with constant stroke
+ scale_x = (w1 - r0w) / (w0 - r0w);
+ scale_y = (h1 - r0h) / (h0 - r0h);
+ unbudge *= Geom::Translate (-flip_x * stroke_ratio_w * r0w * (scale_x - 1), -flip_y * stroke_ratio_h * r0h * (scale_y - 1));
+ } else if (!transform_stroke) { // 'Preserve Transforms' was chosen.
+ // geometric mean of r0w and r0h will be preserved
+ // new_r0w = r0w*sqrt(scale_x/scale_y)
+ // new_r0h = r0h*sqrt(scale_y/scale_x)
+ // scale_x = (w1 - new_r0w)/(w0 - r0w)
+ // scale_y = (h1 - new_r0h)/(h0 - r0h)
+ gdouble A = h1*(w0 - r0w);
+ gdouble B = (h0*r0w - w0*r0h);
+ gdouble C = -w1*(h0 - r0h);
+ gdouble Sx_div_Sy; // Sx_div_Sy = sqrt(scale_x/scale_y)
+ if (B*B - 4*A*C < 0) {
+ g_message("variable stroke scaling error : %d, %d, %f, %f, %f, %f, %f, %f", transform_stroke, preserve, r0w, r0h, w0, h0, w1, h1);
+ } else {
+ Sx_div_Sy = (-B + sqrt(B*B - 4*A*C))/2/A;
+ scale_x = (w1 - r0w*Sx_div_Sy)/(w0 - r0w);
+ scale_y = (h1 - r0h/Sx_div_Sy)/(h0 - r0h);
+ unbudge *= Geom::Translate (-flip_x * stroke_ratio_w * r0w * scale_x * (1.0 - sqrt(1.0/scale_x/scale_y)), -flip_y * stroke_ratio_h * r0h * scale_y * (1.0 - sqrt(1.0/scale_x/scale_y)));
+ }
+ } else { // 'Preserve Transforms' was chosen, and stroke is scaled
+ scale_x = w1 / w0;
+ scale_y = h1 / h0;
+ }
+ }
+
+ // Now we account for mirroring by flipping if needed
+ scale *= Geom::Scale(flip_x * scale_x, flip_y * scale_y);
+
+ return (p2o * scale * unbudge * o2n);
+}
+
+Geom::Rect get_visual_bbox(Geom::OptRect const &initial_geom_bbox, Geom::Affine const &abs_affine, gdouble const initial_strokewidth, bool const transform_stroke)
+{
+ g_assert(initial_geom_bbox);
+
+ // Find the new geometric bounding box; Do this by transforming each corner of
+ // the initial geometric bounding box individually and fitting a new boundingbox
+ // around the transformed corners
+ Geom::Point const p0 = Geom::Point(initial_geom_bbox->corner(0)) * abs_affine;
+ Geom::Rect new_geom_bbox(p0, p0);
+ for (unsigned i = 1 ; i < 4 ; i++) {
+ new_geom_bbox.expandTo(Geom::Point(initial_geom_bbox->corner(i)) * abs_affine);
+ }
+
+ Geom::Rect new_visual_bbox = new_geom_bbox;
+ if (initial_strokewidth > 0 && initial_strokewidth < Geom::infinity()) {
+ if (transform_stroke) {
+ // scale stroke by: sqrt (((w1-r0)/(w0-r0))*((h1-r0)/(h0-r0))) (for visual bboxes, see get_scale_transform_for_stroke)
+ // equals scaling by: sqrt ((w1/w0)*(h1/h0)) for geometrical bboxes
+ // equals scaling by: sqrt (area1/area0) for geometrical bboxes
+ gdouble const new_strokewidth = initial_strokewidth * sqrt (new_geom_bbox.area() / initial_geom_bbox->area());
+ new_visual_bbox.expandBy(0.5 * new_strokewidth);
+ } else {
+ // Do not transform the stroke
+ new_visual_bbox.expandBy(0.5 * initial_strokewidth);
+ }
+ }
+
+ return new_visual_bbox;
+}
+
+/*
+ Local Variables:
+ mode:c++
+ c-file-style:"stroustrup"
+ c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+ indent-tabs-mode:nil
+ fill-column:99
+ End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
generated by cgit v1.2.3 (git 2.39.1) at 2024-07-17 23:19:13 +0000