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BambuStudio/libslic3r/Geometry.cpp

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#include "libslic3r.h"
#include "Exception.hpp"
#include "Geometry.hpp"
#include "ClipperUtils.hpp"
#include "ExPolygon.hpp"
#include "Line.hpp"
#include "clipper.hpp"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <list>
#include <map>
#include <numeric>
#include <set>
#include <utility>
#include <stack>
#include <vector>
#include <boost/algorithm/string/classification.hpp>
#include <boost/algorithm/string/split.hpp>
#include <boost/log/trivial.hpp>
#if defined(_MSC_VER) && defined(__clang__)
#define BOOST_NO_CXX17_HDR_STRING_VIEW
#endif
namespace Slic3r { namespace Geometry {
bool directions_parallel(double angle1, double angle2, double max_diff)
{
double diff = fabs(angle1 - angle2);
max_diff += EPSILON;
return diff < max_diff || fabs(diff - PI) < max_diff;
}
bool directions_perpendicular(double angle1, double angle2, double max_diff)
{
double diff = fabs(angle1 - angle2);
max_diff += EPSILON;
return fabs(diff - 0.5 * PI) < max_diff || fabs(diff - 1.5 * PI) < max_diff;
}
template<class T>
bool contains(const std::vector<T> &vector, const Point &point)
{
for (typename std::vector<T>::const_iterator it = vector.begin(); it != vector.end(); ++it) {
if (it->contains(point)) return true;
}
return false;
}
template bool contains(const ExPolygons &vector, const Point &point);
double rad2deg_dir(double angle)
{
angle = (angle < PI) ? (-angle + PI/2.0) : (angle + PI/2.0);
if (angle < 0) angle += PI;
return rad2deg(angle);
}
void simplify_polygons(const Polygons &polygons, double tolerance, Polygons* retval)
{
Polygons pp;
for (Polygons::const_iterator it = polygons.begin(); it != polygons.end(); ++it) {
Polygon p = *it;
p.points.push_back(p.points.front());
p.points = MultiPoint::_douglas_peucker(p.points, tolerance);
p.points.pop_back();
pp.push_back(p);
}
*retval = Slic3r::simplify_polygons(pp);
}
double linint(double value, double oldmin, double oldmax, double newmin, double newmax)
{
return (value - oldmin) * (newmax - newmin) / (oldmax - oldmin) + newmin;
}
#if 0
// Point with a weight, by which the points are sorted.
// If the points have the same weight, sort them lexicographically by their positions.
struct ArrangeItem {
ArrangeItem() {}
Vec2d pos;
coordf_t weight;
bool operator<(const ArrangeItem &other) const {
return weight < other.weight ||
((weight == other.weight) && (pos(1) < other.pos(1) || (pos(1) == other.pos(1) && pos(0) < other.pos(0))));
}
};
Pointfs arrange(size_t num_parts, const Vec2d &part_size, coordf_t gap, const BoundingBoxf* bed_bounding_box)
{
// Use actual part size (the largest) plus separation distance (half on each side) in spacing algorithm.
const Vec2d cell_size(part_size(0) + gap, part_size(1) + gap);
const BoundingBoxf bed_bbox = (bed_bounding_box != NULL && bed_bounding_box->defined) ?
*bed_bounding_box :
// Bogus bed size, large enough not to trigger the unsufficient bed size error.
BoundingBoxf(
Vec2d(0, 0),
Vec2d(cell_size(0) * num_parts, cell_size(1) * num_parts));
// This is how many cells we have available into which to put parts.
size_t cellw = size_t(floor((bed_bbox.size()(0) + gap) / cell_size(0)));
size_t cellh = size_t(floor((bed_bbox.size()(1) + gap) / cell_size(1)));
if (num_parts > cellw * cellh)
throw Slic3r::InvalidArgument("%zu parts won't fit in your print area!\n", num_parts);
// Get a bounding box of cellw x cellh cells, centered at the center of the bed.
Vec2d cells_size(cellw * cell_size(0) - gap, cellh * cell_size(1) - gap);
Vec2d cells_offset(bed_bbox.center() - 0.5 * cells_size);
BoundingBoxf cells_bb(cells_offset, cells_size + cells_offset);
// List of cells, sorted by distance from center.
std::vector<ArrangeItem> cellsorder(cellw * cellh, ArrangeItem());
for (size_t j = 0; j < cellh; ++ j) {
// Center of the jth row on the bed.
coordf_t cy = linint(j + 0.5, 0., double(cellh), cells_bb.min(1), cells_bb.max(1));
// Offset from the bed center.
coordf_t yd = cells_bb.center()(1) - cy;
for (size_t i = 0; i < cellw; ++ i) {
// Center of the ith column on the bed.
coordf_t cx = linint(i + 0.5, 0., double(cellw), cells_bb.min(0), cells_bb.max(0));
// Offset from the bed center.
coordf_t xd = cells_bb.center()(0) - cx;
// Cell with a distance from the bed center.
ArrangeItem &ci = cellsorder[j * cellw + i];
// Cell center
ci.pos(0) = cx;
ci.pos(1) = cy;
// Square distance of the cell center to the bed center.
ci.weight = xd * xd + yd * yd;
}
}
// Sort the cells lexicographically by their distances to the bed center and left to right / bttom to top.
std::sort(cellsorder.begin(), cellsorder.end());
cellsorder.erase(cellsorder.begin() + num_parts, cellsorder.end());
// Return the (left,top) corners of the cells.
Pointfs positions;
positions.reserve(num_parts);
for (std::vector<ArrangeItem>::const_iterator it = cellsorder.begin(); it != cellsorder.end(); ++ it)
positions.push_back(Vec2d(it->pos(0) - 0.5 * part_size(0), it->pos(1) - 0.5 * part_size(1)));
return positions;
}
#else
class ArrangeItem {
public:
Vec2d pos = Vec2d::Zero();
size_t index_x, index_y;
coordf_t dist;
};
class ArrangeItemIndex {
public:
coordf_t index;
ArrangeItem item;
ArrangeItemIndex(coordf_t _index, ArrangeItem _item) : index(_index), item(_item) {};
};
bool
arrange(size_t total_parts, const Vec2d &part_size, coordf_t dist, const BoundingBoxf* bb, Pointfs &positions)
{
positions.clear();
Vec2d part = part_size;
// use actual part size (the largest) plus separation distance (half on each side) in spacing algorithm
part(0) += dist;
part(1) += dist;
Vec2d area(Vec2d::Zero());
if (bb != NULL && bb->defined) {
area = bb->size();
} else {
// bogus area size, large enough not to trigger the error below
area(0) = part(0) * total_parts;
area(1) = part(1) * total_parts;
}
// this is how many cells we have available into which to put parts
size_t cellw = floor((area(0) + dist) / part(0));
size_t cellh = floor((area(1) + dist) / part(1));
if (total_parts > (cellw * cellh))
return false;
// total space used by cells
Vec2d cells(cellw * part(0), cellh * part(1));
// bounding box of total space used by cells
BoundingBoxf cells_bb;
cells_bb.merge(Vec2d(0,0)); // min
cells_bb.merge(cells); // max
// center bounding box to area
cells_bb.translate(
(area(0) - cells(0)) / 2,
(area(1) - cells(1)) / 2
);
// list of cells, sorted by distance from center
std::vector<ArrangeItemIndex> cellsorder;
// work out distance for all cells, sort into list
for (size_t i = 0; i <= cellw-1; ++i) {
for (size_t j = 0; j <= cellh-1; ++j) {
coordf_t cx = linint(i + 0.5, 0, cellw, cells_bb.min(0), cells_bb.max(0));
coordf_t cy = linint(j + 0.5, 0, cellh, cells_bb.min(1), cells_bb.max(1));
coordf_t xd = fabs((area(0) / 2) - cx);
coordf_t yd = fabs((area(1) / 2) - cy);
ArrangeItem c;
c.pos(0) = cx;
c.pos(1) = cy;
c.index_x = i;
c.index_y = j;
c.dist = xd * xd + yd * yd - fabs((cellw / 2) - (i + 0.5));
// binary insertion sort
{
coordf_t index = c.dist;
size_t low = 0;
size_t high = cellsorder.size();
while (low < high) {
size_t mid = (low + ((high - low) / 2)) | 0;
coordf_t midval = cellsorder[mid].index;
if (midval < index) {
low = mid + 1;
} else if (midval > index) {
high = mid;
} else {
cellsorder.insert(cellsorder.begin() + mid, ArrangeItemIndex(index, c));
goto ENDSORT;
}
}
cellsorder.insert(cellsorder.begin() + low, ArrangeItemIndex(index, c));
}
ENDSORT: ;
}
}
// the extents of cells actually used by objects
coordf_t lx = 0;
coordf_t ty = 0;
coordf_t rx = 0;
coordf_t by = 0;
// now find cells actually used by objects, map out the extents so we can position correctly
for (size_t i = 1; i <= total_parts; ++i) {
ArrangeItemIndex c = cellsorder[i - 1];
coordf_t cx = c.item.index_x;
coordf_t cy = c.item.index_y;
if (i == 1) {
lx = rx = cx;
ty = by = cy;
} else {
if (cx > rx) rx = cx;
if (cx < lx) lx = cx;
if (cy > by) by = cy;
if (cy < ty) ty = cy;
}
}
// now we actually place objects into cells, positioned such that the left and bottom borders are at 0
for (size_t i = 1; i <= total_parts; ++i) {
ArrangeItemIndex c = cellsorder.front();
cellsorder.erase(cellsorder.begin());
coordf_t cx = c.item.index_x - lx;
coordf_t cy = c.item.index_y - ty;
positions.push_back(Vec2d(cx * part(0), cy * part(1)));
}
if (bb != NULL && bb->defined) {
for (Pointfs::iterator p = positions.begin(); p != positions.end(); ++p) {
p->x() += bb->min(0);
p->y() += bb->min(1);
}
}
return true;
}
#endif
// Euclidian distance of two boost::polygon points.
template<typename T>
T dist(const boost::polygon::point_data<T> &p1,const boost::polygon::point_data<T> &p2)
{
T dx = p2(0) - p1(0);
T dy = p2(1) - p1(1);
return sqrt(dx*dx+dy*dy);
}
// Find a foot point of "px" on a segment "seg".
template<typename segment_type, typename point_type>
inline point_type project_point_to_segment(segment_type &seg, point_type &px)
{
typedef typename point_type::coordinate_type T;
const point_type &p0 = low(seg);
const point_type &p1 = high(seg);
const point_type dir(p1(0)-p0(0), p1(1)-p0(1));
const point_type dproj(px(0)-p0(0), px(1)-p0(1));
const T t = (dir(0)*dproj(0) + dir(1)*dproj(1)) / (dir(0)*dir(0) + dir(1)*dir(1));
assert(t >= T(-1e-6) && t <= T(1. + 1e-6));
return point_type(p0(0) + t*dir(0), p0(1) + t*dir(1));
}
void assemble_transform(Transform3d& transform, const Vec3d& translation, const Vec3d& rotation, const Vec3d& scale, const Vec3d& mirror)
{
transform = Transform3d::Identity();
transform.translate(translation);
transform.rotate(Eigen::AngleAxisd(rotation(2), Vec3d::UnitZ()) * Eigen::AngleAxisd(rotation(1), Vec3d::UnitY()) * Eigen::AngleAxisd(rotation(0), Vec3d::UnitX()));
transform.scale(scale.cwiseProduct(mirror));
}
Transform3d assemble_transform(const Vec3d& translation, const Vec3d& rotation, const Vec3d& scale, const Vec3d& mirror)
{
Transform3d transform;
assemble_transform(transform, translation, rotation, scale, mirror);
return transform;
}
Vec3d extract_euler_angles(const Eigen::Matrix<double, 3, 3, Eigen::DontAlign>& rotation_matrix)
{
// The extracted "rotation" is a triplet of numbers such that Geometry::rotation_transform
// returns the original transform. Because of the chosen order of rotations, the triplet
// is not equivalent to Euler angles in the usual sense.
Vec3d angles = rotation_matrix.eulerAngles(2, 1, 0);
std::swap(angles(0), angles(2));
return angles;
}
Vec3d extract_euler_angles(const Transform3d& transform)
{
// use only the non-translational part of the transform
Eigen::Matrix<double, 3, 3, Eigen::DontAlign> m = transform.matrix().block(0, 0, 3, 3);
// remove scale
m.col(0).normalize();
m.col(1).normalize();
m.col(2).normalize();
return extract_euler_angles(m);
}
void rotation_from_two_vectors(Vec3d from, Vec3d to, Vec3d& rotation_axis, double& phi, Matrix3d* rotation_matrix)
{
const Matrix3d m = Eigen::Quaterniond().setFromTwoVectors(from, to).toRotationMatrix();
const Eigen::AngleAxisd aa(m);
rotation_axis = aa.axis();
phi = aa.angle();
if (rotation_matrix)
*rotation_matrix = m;
}
Transform3d translation_transform(const Vec3d &translation)
{
Transform3d transform = Transform3d::Identity();
transform.translate(translation);
return transform;
}
Transform3d rotation_transform(const Vec3d& rotation)
{
Transform3d transform = Transform3d::Identity();
transform.rotate(Eigen::AngleAxisd(rotation.z(), Vec3d::UnitZ()) * Eigen::AngleAxisd(rotation.y(), Vec3d::UnitY()) * Eigen::AngleAxisd(rotation.x(), Vec3d::UnitX()));
return transform;
}
void scale_transform(Transform3d &transform, double scale) {
return scale_transform(transform, scale * Vec3d::Ones());
}
void scale_transform(Transform3d &transform, const Vec3d &scale)
{
transform = Transform3d::Identity();
transform.scale(scale);
}
Transform3d scale_transform(double scale) {
return scale_transform(scale * Vec3d::Ones());
}
Transform3d scale_transform(const Vec3d &scale)
{
Transform3d transform;
scale_transform(transform, scale);
return transform;
}
Transformation::Flags::Flags()
: dont_translate(true)
, dont_rotate(true)
, dont_scale(true)
, dont_mirror(true)
{
}
bool Transformation::Flags::needs_update(bool dont_translate, bool dont_rotate, bool dont_scale, bool dont_mirror) const
{
return (this->dont_translate != dont_translate) || (this->dont_rotate != dont_rotate) || (this->dont_scale != dont_scale) || (this->dont_mirror != dont_mirror);
}
void Transformation::Flags::set(bool dont_translate, bool dont_rotate, bool dont_scale, bool dont_mirror)
{
this->dont_translate = dont_translate;
this->dont_rotate = dont_rotate;
this->dont_scale = dont_scale;
this->dont_mirror = dont_mirror;
}
Transformation::Transformation()
{
reset();
}
Transformation::Transformation(const Transform3d& transform)
{
set_from_transform(transform);
}
Transform3d Transformation::get_offset_matrix() const {
return translation_transform(get_offset());
}
void Transformation::set_offset(const Vec3d &offset)
{
set_offset(X, offset(0));
set_offset(Y, offset(1));
set_offset(Z, offset(2));
}
void Transformation::set_offset(Axis axis, double offset)
{
if (m_offset(axis) != offset)
{
m_offset(axis) = offset;
m_dirty = true;
}
}
static Transform3d extract_rotation_matrix(const Transform3d &trafo)
{
Matrix3d rotation;
Matrix3d scale;
trafo.computeRotationScaling(&rotation, &scale);
return Transform3d(rotation);
}
static Transform3d extract_scale(const Transform3d &trafo)
{
Matrix3d rotation;
Matrix3d scale;
trafo.computeRotationScaling(&rotation, &scale);
return Transform3d(scale);
}
Transform3d Transformation::get_rotation_matrix() const {
return extract_rotation_matrix(m_matrix);
}
void Transformation::set_rotation(const Vec3d &rotation)
{
set_rotation(X, rotation(0));
set_rotation(Y, rotation(1));
set_rotation(Z, rotation(2));
}
void Transformation::set_rotation(Axis axis, double rotation)
{
rotation = angle_to_0_2PI(rotation);
if (is_approx(std::abs(rotation), 2.0 * (double)PI))
rotation = 0.0;
if (m_rotation(axis) != rotation)
{
m_rotation(axis) = rotation;
m_dirty = true;
}
}
Transform3d Transformation::get_scaling_factor_matrix() const
{
Transform3d scale = extract_scale(m_matrix);
scale(0, 0) = std::abs(scale(0, 0));
scale(1, 1) = std::abs(scale(1, 1));
scale(2, 2) = std::abs(scale(2, 2));
return scale;
}
void Transformation::set_scaling_factor(const Vec3d& scaling_factor)
{
set_scaling_factor(X, scaling_factor(0));
set_scaling_factor(Y, scaling_factor(1));
set_scaling_factor(Z, scaling_factor(2));
}
void Transformation::set_scaling_factor(Axis axis, double scaling_factor)
{
if (m_scaling_factor(axis) != std::abs(scaling_factor))
{
m_scaling_factor(axis) = std::abs(scaling_factor);
m_dirty = true;
}
}
void Transformation::set_mirror(const Vec3d& mirror)
{
set_mirror(X, mirror(0));
set_mirror(Y, mirror(1));
set_mirror(Z, mirror(2));
}
void Transformation::set_mirror(Axis axis, double mirror)
{
double abs_mirror = std::abs(mirror);
if (abs_mirror == 0.0)
mirror = 1.0;
else if (abs_mirror != 1.0)
mirror /= abs_mirror;
if (m_mirror(axis) != mirror)
{
m_mirror(axis) = mirror;
m_dirty = true;
}
}
void Transformation::set_from_transform(const Transform3d& transform)
{
// offset
set_offset(transform.matrix().block(0, 3, 3, 1));
Eigen::Matrix<double, 3, 3, Eigen::DontAlign> m3x3 = transform.matrix().block(0, 0, 3, 3);
// mirror
// it is impossible to reconstruct the original mirroring factors from a matrix,
// we can only detect if the matrix contains a left handed reference system
// in which case we reorient it back to right handed by mirroring the x axis
Vec3d mirror = Vec3d::Ones();
if (m3x3.col(0).dot(m3x3.col(1).cross(m3x3.col(2))) < 0.0)
{
mirror(0) = -1.0;
// remove mirror
m3x3.col(0) *= -1.0;
}
set_mirror(mirror);
// scale
set_scaling_factor(Vec3d(m3x3.col(0).norm(), m3x3.col(1).norm(), m3x3.col(2).norm()));
// remove scale
m3x3.col(0).normalize();
m3x3.col(1).normalize();
m3x3.col(2).normalize();
// rotation
set_rotation(Geometry::extract_euler_angles(m3x3));
// forces matrix recalculation matrix
m_matrix = get_matrix();
// // debug check
// if (!m_matrix.isApprox(transform))
// std::cout << "something went wrong in extracting data from matrix" << std::endl;
}
void Transformation::reset()
{
m_offset = Vec3d::Zero();
m_rotation = Vec3d::Zero();
m_scaling_factor = Vec3d::Ones();
m_mirror = Vec3d::Ones();
m_matrix = Transform3d::Identity();
m_dirty = false;
}
void Transformation::reset_rotation() {
const Geometry::TransformationSVD svd(*this);
m_matrix = get_offset_matrix() * Transform3d(svd.v * svd.s * svd.v.transpose()) * svd.mirror_matrix();
}
void Transformation::reset_scaling_factor() {
const Geometry::TransformationSVD svd(*this);
m_matrix = get_offset_matrix() * Transform3d(svd.u) * Transform3d(svd.v.transpose()) * svd.mirror_matrix();
}
void Transformation::reset_skew() {
auto new_scale_factor = [](const Matrix3d &s) {
return pow(s(0, 0) * s(1, 1) * s(2, 2), 1. / 3.); // scale average
};
const Geometry::TransformationSVD svd(*this);
m_matrix = get_offset_matrix() * Transform3d(svd.u) * scale_transform(new_scale_factor(svd.s)) * Transform3d(svd.v.transpose()) * svd.mirror_matrix();
}
const Transform3d& Transformation::get_matrix(bool dont_translate, bool dont_rotate, bool dont_scale, bool dont_mirror) const
{
if (m_dirty || m_flags.needs_update(dont_translate, dont_rotate, dont_scale, dont_mirror))
{
m_matrix = Geometry::assemble_transform(
dont_translate ? Vec3d::Zero() : m_offset,
dont_rotate ? Vec3d::Zero() : m_rotation,
dont_scale ? Vec3d::Ones() : m_scaling_factor,
dont_mirror ? Vec3d::Ones() : m_mirror
);
m_flags.set(dont_translate, dont_rotate, dont_scale, dont_mirror);
m_dirty = false;
}
return m_matrix;
}
Transform3d Transformation::get_matrix_no_offset() const
{
Transformation copy(*this);
copy.reset_offset();
return copy.get_matrix();
}
Transform3d Transformation::get_matrix_no_scaling_factor() const
{
Transformation copy(*this);
copy.reset_scaling_factor();
return copy.get_matrix();
}
Transformation Transformation::operator * (const Transformation& other) const
{
return Transformation(get_matrix() * other.get_matrix());
}
Transformation Transformation::volume_to_bed_transformation(const Transformation& instance_transformation, const BoundingBoxf3& bbox)
{
Transformation out;
if (instance_transformation.is_scaling_uniform()) {
// No need to run the non-linear least squares fitting for uniform scaling.
// Just set the inverse.
out.set_from_transform(instance_transformation.get_matrix(true).inverse());
}
else if (is_rotation_ninety_degrees(instance_transformation.get_rotation()))
{
// Anisotropic scaling, rotation by multiples of ninety degrees.
Eigen::Matrix3d instance_rotation_trafo =
(Eigen::AngleAxisd(instance_transformation.get_rotation().z(), Vec3d::UnitZ()) *
Eigen::AngleAxisd(instance_transformation.get_rotation().y(), Vec3d::UnitY()) *
Eigen::AngleAxisd(instance_transformation.get_rotation().x(), Vec3d::UnitX())).toRotationMatrix();
Eigen::Matrix3d volume_rotation_trafo =
(Eigen::AngleAxisd(-instance_transformation.get_rotation().x(), Vec3d::UnitX()) *
Eigen::AngleAxisd(-instance_transformation.get_rotation().y(), Vec3d::UnitY()) *
Eigen::AngleAxisd(-instance_transformation.get_rotation().z(), Vec3d::UnitZ())).toRotationMatrix();
// 8 corners of the bounding box.
auto pts = Eigen::MatrixXd(8, 3);
pts(0, 0) = bbox.min.x(); pts(0, 1) = bbox.min.y(); pts(0, 2) = bbox.min.z();
pts(1, 0) = bbox.min.x(); pts(1, 1) = bbox.min.y(); pts(1, 2) = bbox.max.z();
pts(2, 0) = bbox.min.x(); pts(2, 1) = bbox.max.y(); pts(2, 2) = bbox.min.z();
pts(3, 0) = bbox.min.x(); pts(3, 1) = bbox.max.y(); pts(3, 2) = bbox.max.z();
pts(4, 0) = bbox.max.x(); pts(4, 1) = bbox.min.y(); pts(4, 2) = bbox.min.z();
pts(5, 0) = bbox.max.x(); pts(5, 1) = bbox.min.y(); pts(5, 2) = bbox.max.z();
pts(6, 0) = bbox.max.x(); pts(6, 1) = bbox.max.y(); pts(6, 2) = bbox.min.z();
pts(7, 0) = bbox.max.x(); pts(7, 1) = bbox.max.y(); pts(7, 2) = bbox.max.z();
// Corners of the bounding box transformed into the modifier mesh coordinate space, with inverse rotation applied to the modifier.
auto qs = pts *
(instance_rotation_trafo *
Eigen::Scaling(instance_transformation.get_scaling_factor().cwiseProduct(instance_transformation.get_mirror())) *
volume_rotation_trafo).inverse().transpose();
// Fill in scaling based on least squares fitting of the bounding box corners.
Vec3d scale;
for (int i = 0; i < 3; ++i)
scale(i) = pts.col(i).dot(qs.col(i)) / pts.col(i).dot(pts.col(i));
out.set_rotation(Geometry::extract_euler_angles(volume_rotation_trafo));
out.set_scaling_factor(Vec3d(std::abs(scale(0)), std::abs(scale(1)), std::abs(scale(2))));
out.set_mirror(Vec3d(scale(0) > 0 ? 1. : -1, scale(1) > 0 ? 1. : -1, scale(2) > 0 ? 1. : -1));
}
else
{
// General anisotropic scaling, general rotation.
// Keep the modifier mesh in the instance coordinate system, so the modifier mesh will not be aligned with the world.
// Scale it to get the required size.
out.set_scaling_factor(instance_transformation.get_scaling_factor().cwiseInverse());
}
return out;
}
// For parsing a transformation matrix from 3MF / AMF.
Transform3d transform3d_from_string(const std::string& transform_str)
{
assert(is_decimal_separator_point()); // for atof
Transform3d transform = Transform3d::Identity();
if (!transform_str.empty())
{
std::vector<std::string> mat_elements_str;
boost::split(mat_elements_str, transform_str, boost::is_any_of(" "), boost::token_compress_on);
unsigned int size = (unsigned int)mat_elements_str.size();
if (size == 16)
{
unsigned int i = 0;
for (unsigned int r = 0; r < 4; ++r)
{
for (unsigned int c = 0; c < 4; ++c)
{
transform(r, c) = ::atof(mat_elements_str[i++].c_str());
}
}
}
}
return transform;
}
Eigen::Quaterniond rotation_xyz_diff(const Vec3d &rot_xyz_from, const Vec3d &rot_xyz_to)
{
return
// From the current coordinate system to world.
Eigen::AngleAxisd(rot_xyz_to(2), Vec3d::UnitZ()) * Eigen::AngleAxisd(rot_xyz_to(1), Vec3d::UnitY()) * Eigen::AngleAxisd(rot_xyz_to(0), Vec3d::UnitX()) *
// From world to the initial coordinate system.
Eigen::AngleAxisd(-rot_xyz_from(0), Vec3d::UnitX()) * Eigen::AngleAxisd(-rot_xyz_from(1), Vec3d::UnitY()) * Eigen::AngleAxisd(-rot_xyz_from(2), Vec3d::UnitZ());
}
// This should only be called if it is known, that the two rotations only differ in rotation around the Z axis.
double rotation_diff_z(const Vec3d &rot_xyz_from, const Vec3d &rot_xyz_to)
{
Eigen::AngleAxisd angle_axis(rotation_xyz_diff(rot_xyz_from, rot_xyz_to));
Vec3d axis = angle_axis.axis();
double angle = angle_axis.angle();
#ifndef NDEBUG
if (std::abs(angle) > 1e-8) {
assert(std::abs(axis.x()) < 1e-8);
assert(std::abs(axis.y()) < 1e-8);
}
#endif /* NDEBUG */
return (axis.z() < 0) ? -angle : angle;
}
Geometry::TransformationSVD::TransformationSVD(const Transform3d &trafo)
{
const auto &m0 = trafo.matrix().block<3, 3>(0, 0);
mirror = m0.determinant() < 0.0;
Matrix3d m;
if (mirror)
m = m0 * Eigen::DiagonalMatrix<double, 3, 3>(-1.0, 1.0, 1.0);
else
m = m0;
const Eigen::JacobiSVD<Matrix3d> svd(m, Eigen::ComputeFullU | Eigen::ComputeFullV);
u = svd.matrixU();
v = svd.matrixV();
s = svd.singularValues().asDiagonal();
scale = !s.isApprox(Matrix3d::Identity());
anisotropic_scale = !is_approx(s(0, 0), s(1, 1)) || !is_approx(s(1, 1), s(2, 2));
rotation = !v.isApprox(u);
if (anisotropic_scale) {
rotation_90_degrees = true;
for (int i = 0; i < 3; ++i) {
const Vec3d row = v.row(i).cwiseAbs();
const size_t num_zeros = is_approx(row[0], 0.) + is_approx(row[1], 0.) + is_approx(row[2], 0.);
const size_t num_ones = is_approx(row[0], 1.) + is_approx(row[1], 1.) + is_approx(row[2], 1.);
if (num_zeros != 2 || num_ones != 1) {
rotation_90_degrees = false;
break;
}
}
// Detect skew by brute force: check if the axes are still orthogonal after transformation
const Matrix3d trafo_linear = trafo.linear();
const std::array<Vec3d, 3> axes = {Vec3d::UnitX(), Vec3d::UnitY(), Vec3d::UnitZ()};
std::array<Vec3d, 3> transformed_axes;
for (int i = 0; i < 3; ++i) { transformed_axes[i] = trafo_linear * axes[i]; }
skew = std::abs(transformed_axes[0].dot(transformed_axes[1])) > EPSILON || std::abs(transformed_axes[1].dot(transformed_axes[2])) > EPSILON ||
std::abs(transformed_axes[2].dot(transformed_axes[0])) > EPSILON;
// This following old code does not work under all conditions. The v matrix can become non diagonal (see SPE-1492)
// skew = ! rotation_90_degrees;
} else
skew = false;
}
Transformation mat_around_a_point_rotate(const Transformation &InMat, const Vec3d &pt, const Vec3d &axis, float rotate_theta_radian)
{
auto xyz = InMat.get_offset();
Transformation left;
left.set_offset(-xyz); // at world origin
auto curMat = left * InMat;
auto qua = Eigen::Quaterniond(Eigen::AngleAxisd(rotate_theta_radian, axis));
qua.normalize();
Transform3d cur_matrix;
Transformation rotateMat4;
rotateMat4.set_from_transform(cur_matrix.fromPositionOrientationScale(Vec3d(0., 0., 0.), qua, Vec3d(1., 1., 1.)));
curMat = rotateMat4 * curMat; // along_fix_axis
// rotate mat4 along fix pt
Transformation temp_world;
auto qua_world = Eigen::Quaterniond(Eigen::AngleAxisd(0, axis));
qua_world.normalize();
Transform3d cur_matrix_world;
temp_world.set_from_transform(cur_matrix_world.fromPositionOrientationScale(pt, qua_world, Vec3d(1., 1., 1.)));
auto temp_xyz = temp_world.get_matrix().inverse() * xyz;
auto new_pos = temp_world.get_matrix() * (rotateMat4.get_matrix() * temp_xyz);
curMat.set_offset(new_pos);
return curMat;
}
} // namespace Geometry
} // namespace Slic3r
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