Replaced the repeated application of Cursors (Sphere or Circle) in painting using 2D and 3D Capsules.
Previously, the Cursor (Sphere or Circle) was repeatedly applied between two mouse positions, creating brushstrokes with ripples on the edges between those mouse positions. Now, a single capsule (3D or 2D) is applied between those mouse positions, which creates brushstrokes without these ripples.
This commit is contained in:
Lukáš Hejl
parent
e898eda320
commit
7bb38840e1
6 changed files with 558 additions and 69 deletions
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@ -9,6 +9,112 @@
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namespace Slic3r {
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// Check if the line is whole inside the sphere, or it is partially inside (intersecting) the sphere.
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// Inspired by Christer Ericson's Real-Time Collision Detection, pp. 177-179.
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static bool test_line_inside_sphere(const Vec3f &line_a, const Vec3f &line_b, const Vec3f &sphere_p, const float sphere_radius)
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{
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const float sphere_radius_sqr = Slic3r::sqr(sphere_radius);
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const Vec3f line_dir = line_b - line_a; // n
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const Vec3f origins_diff = line_a - sphere_p; // m
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const float m_dot_m = origins_diff.dot(origins_diff);
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// Check if any of the end-points of the line is inside the sphere.
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if (m_dot_m <= sphere_radius_sqr || (line_b - sphere_p).squaredNorm() <= sphere_radius_sqr)
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return true;
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// Check if the infinite line is going through the sphere.
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const float n_dot_n = line_dir.dot(line_dir);
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const float m_dot_n = origins_diff.dot(line_dir);
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const float eq_a = n_dot_n;
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const float eq_b = m_dot_n;
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const float eq_c = m_dot_m - sphere_radius_sqr;
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const float discr = eq_b * eq_b - eq_a * eq_c;
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// A negative discriminant corresponds to the infinite line infinite not going through the sphere.
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if (discr < 0.f)
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return false;
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// Check if the finite line is going through the sphere.
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const float discr_sqrt = std::sqrt(discr);
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const float t1 = (-eq_b - discr_sqrt) / eq_a;
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if (0.f <= t1 && t1 <= 1.f)
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return true;
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const float t2 = (-eq_b + discr_sqrt) / eq_a;
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if (0.f <= t2 && t2 <= 1.f && discr_sqrt > 0.f)
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return true;
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return false;
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}
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// Check if the line is whole inside the finite cylinder, or it is partially inside (intersecting) the finite cylinder.
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// Inspired by Christer Ericson's Real-Time Collision Detection, pp. 194-198.
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static bool test_line_inside_cylinder(const Vec3f &line_a, const Vec3f &line_b, const Vec3f &cylinder_P, const Vec3f &cylinder_Q, const float cylinder_radius)
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{
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assert(cylinder_P != cylinder_Q);
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const Vec3f cylinder_dir = cylinder_Q - cylinder_P; // d
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auto is_point_inside_finite_cylinder = [&cylinder_P, &cylinder_Q, &cylinder_radius, &cylinder_dir](const Vec3f &pt) {
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const Vec3f first_center_diff = cylinder_P - pt;
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const Vec3f second_center_diff = cylinder_Q - pt;
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// First, check if the point pt is laying between planes defined by cylinder_p and cylinder_q.
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// Then check if it is inside the cylinder between cylinder_p and cylinder_q.
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return first_center_diff.dot(cylinder_dir) <= 0 && second_center_diff.dot(cylinder_dir) >= 0 &&
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(first_center_diff.cross(cylinder_dir).norm() / cylinder_dir.norm()) <= cylinder_radius;
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};
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// Check if any of the end-points of the line is inside the cylinder.
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if (is_point_inside_finite_cylinder(line_a) || is_point_inside_finite_cylinder(line_b))
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return true;
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// Check if the line is going through the cylinder.
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const Vec3f origins_diff = line_a - cylinder_P; // m
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const Vec3f line_dir = line_b - line_a; // n
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const float m_dot_d = origins_diff.dot(cylinder_dir);
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const float n_dot_d = line_dir.dot(cylinder_dir);
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const float d_dot_d = cylinder_dir.dot(cylinder_dir);
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const float n_dot_n = line_dir.dot(line_dir);
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const float m_dot_n = origins_diff.dot(line_dir);
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const float m_dot_m = origins_diff.dot(origins_diff);
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const float eq_a = d_dot_d * n_dot_n - n_dot_d * n_dot_d;
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const float eq_b = d_dot_d * m_dot_n - n_dot_d * m_dot_d;
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const float eq_c = d_dot_d * (m_dot_m - Slic3r::sqr(cylinder_radius)) - m_dot_d * m_dot_d;
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const float discr = eq_b * eq_b - eq_a * eq_c;
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// A negative discriminant corresponds to the infinite line not going through the infinite cylinder.
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if (discr < 0.0f)
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return false;
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// Check if the finite line is going through the finite cylinder.
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const float discr_sqrt = std::sqrt(discr);
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const float t1 = (-eq_b - discr_sqrt) / eq_a;
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if (0.f <= t1 && t1 <= 1.f)
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if (const float cylinder_endcap_t1 = m_dot_d + t1 * n_dot_d; 0.f <= cylinder_endcap_t1 && cylinder_endcap_t1 <= d_dot_d)
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return true;
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const float t2 = (-eq_b + discr_sqrt) / eq_a;
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if (0.f <= t2 && t2 <= 1.f)
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if (const float cylinder_endcap_t2 = (m_dot_d + t2 * n_dot_d); 0.f <= cylinder_endcap_t2 && cylinder_endcap_t2 <= d_dot_d)
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return true;
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return false;
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}
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// Check if the line is whole inside the capsule, or it is partially inside (intersecting) the capsule.
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static bool test_line_inside_capsule(const Vec3f &line_a, const Vec3f &line_b, const Vec3f &capsule_p, const Vec3f &capsule_q, const float capsule_radius) {
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assert(capsule_p != capsule_q);
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// Check if the line intersect any of the spheres forming the capsule.
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if (test_line_inside_sphere(line_a, line_b, capsule_p, capsule_radius) || test_line_inside_sphere(line_a, line_b, capsule_q, capsule_radius))
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return true;
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// Check if the line intersects the cylinder between the centers of the spheres.
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return test_line_inside_cylinder(line_a, line_b, capsule_p, capsule_q, capsule_radius);
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}
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#ifndef NDEBUG
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bool TriangleSelector::verify_triangle_midpoints(const Triangle &tr) const
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{
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@ -902,13 +1008,13 @@ bool TriangleSelector::Cursor::is_pointer_in_triangle(const Triangle &tr, const
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}
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// Determine whether this facet is potentially visible (still can be obscured).
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bool TriangleSelector::Circle::is_facet_visible(int facet_idx, const std::vector<Vec3f> &face_normals) const
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bool TriangleSelector::Cursor::is_facet_visible(const Cursor &cursor, int facet_idx, const std::vector<Vec3f> &face_normals)
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{
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assert(facet_idx < int(face_normals.size()));
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Vec3f n = face_normals[facet_idx];
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if (!this->uniform_scaling)
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n = this->trafo_normal * n;
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return n.dot(this->dir) < 0.f;
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if (!cursor.uniform_scaling)
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n = cursor.trafo_normal * n;
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return n.dot(cursor.dir) < 0.f;
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}
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// How many vertices of a triangle are inside the circle?
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@ -922,8 +1028,27 @@ int TriangleSelector::Cursor::vertices_inside(const Triangle &tr, const std::vec
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return inside;
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}
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// Is any edge inside Sphere cursor?
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bool TriangleSelector::Sphere::is_edge_inside_cursor(const Triangle &tr, const std::vector<Vertex> &vertices) const
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{
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std::array<Vec3f, 3> pts;
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for (int i = 0; i < 3; ++i) {
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pts[i] = vertices[tr.verts_idxs[i]].v;
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if (!this->uniform_scaling)
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pts[i] = this->trafo * pts[i];
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}
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for (int side = 0; side < 3; ++side) {
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const Vec3f &edge_a = pts[side];
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const Vec3f &edge_b = pts[side < 2 ? side + 1 : 0];
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if (test_line_inside_sphere(edge_a, edge_b, this->center, this->radius))
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return true;
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}
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return false;
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}
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// Is edge inside cursor?
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bool TriangleSelector::SinglePointCursor::is_edge_inside_cursor(const Triangle &tr, const std::vector<Vertex> &vertices) const
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bool TriangleSelector::Circle::is_edge_inside_cursor(const Triangle &tr, const std::vector<Vertex> &vertices) const
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{
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std::array<Vec3f, 3> pts;
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for (int i = 0; i < 3; ++i) {
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@ -933,7 +1058,6 @@ bool TriangleSelector::SinglePointCursor::is_edge_inside_cursor(const Triangle &
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}
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const Vec3f &p = this->center;
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for (int side = 0; side < 3; ++side) {
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const Vec3f &a = pts[side];
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const Vec3f &b = pts[side < 2 ? side + 1 : 0];
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@ -1675,7 +1799,8 @@ TriangleSelector::Cursor::Cursor(const Vec3f &source_, float radius_world, const
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{
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Vec3d sf = Geometry::Transformation(trafo_).get_scaling_factor();
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if (is_approx(sf(0), sf(1)) && is_approx(sf(1), sf(2))) {
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radius_sqr = float(std::pow(radius_world / sf(0), 2));
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radius = float(radius_world / sf(0));
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radius_sqr = float(Slic3r::sqr(radius_world / sf(0)));
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uniform_scaling = true;
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} else {
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// In case that the transformation is non-uniform, all checks whether
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@ -1683,7 +1808,8 @@ TriangleSelector::Cursor::Cursor(const Vec3f &source_, float radius_world, const
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// First transform source in world coords and remember that we did this.
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source = trafo * source;
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uniform_scaling = false;
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radius_sqr = radius_world * radius_world;
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radius = radius_world;
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radius_sqr = Slic3r::sqr(radius_world);
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trafo_normal = trafo.linear().inverse().transpose();
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}
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}
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@ -1701,16 +1827,32 @@ TriangleSelector::SinglePointCursor::SinglePointCursor(const Vec3f& center_, con
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dir = (center - source).normalized();
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}
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TriangleSelector::DoublePointCursor::DoublePointCursor(const Vec3f &first_center_, const Vec3f &second_center_, const Vec3f &source_, float radius_world, const Transform3d &trafo_, const ClippingPlane &clipping_plane_)
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: first_center{first_center_}, second_center{second_center_}, Cursor(source_, radius_world, trafo_, clipping_plane_)
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{
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if (!uniform_scaling) {
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first_center = trafo * first_center_;
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second_center = trafo * second_center_;
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}
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// Calculate dir, in whatever coords is appropriate.
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dir = (first_center - source).normalized();
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}
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// Returns true if clipping plane is not active or if the point not clipped by clipping plane.
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inline static bool is_mesh_point_not_clipped(const Vec3f &point, const TriangleSelector::ClippingPlane &clipping_plane)
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{
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return !clipping_plane.is_active() || !clipping_plane.is_mesh_point_clipped(point);
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}
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// Is a point (in mesh coords) inside a Sphere cursor?
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bool TriangleSelector::Sphere::is_mesh_point_inside(const Vec3f &point) const
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{
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const Vec3f transformed_point = uniform_scaling ? point : Vec3f(trafo * point);
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const bool is_point_inside = (center - point).squaredNorm() < radius_sqr;
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if ((center - transformed_point).squaredNorm() < radius_sqr)
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return is_mesh_point_not_clipped(point, clipping_plane);
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if (is_point_inside && clipping_plane.is_active())
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return !clipping_plane.is_mesh_point_clipped(point);
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return is_point_inside;
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return false;
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}
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// Is a point (in mesh coords) inside a Circle cursor?
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@ -1718,12 +1860,62 @@ bool TriangleSelector::Circle::is_mesh_point_inside(const Vec3f &point) const
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{
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const Vec3f transformed_point = uniform_scaling ? point : Vec3f(trafo * point);
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const Vec3f diff = center - transformed_point;
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const bool is_point_inside = (diff - diff.dot(dir) * dir).squaredNorm() < radius_sqr;
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if (is_point_inside && clipping_plane.is_active())
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return !clipping_plane.is_mesh_point_clipped(point);
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if ((diff - diff.dot(dir) * dir).squaredNorm() < radius_sqr)
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return is_mesh_point_not_clipped(point, clipping_plane);
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return is_point_inside;
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return false;
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}
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// Is a point (in mesh coords) inside a Capsule3D cursor?
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bool TriangleSelector::Capsule3D::is_mesh_point_inside(const Vec3f &point) const
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{
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const Vec3f transformed_point = uniform_scaling ? point : Vec3f(trafo * point);
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const Vec3f first_center_diff = this->first_center - transformed_point;
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const Vec3f second_center_diff = this->second_center - transformed_point;
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if (first_center_diff.squaredNorm() < this->radius_sqr || second_center_diff.squaredNorm() < this->radius_sqr)
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return is_mesh_point_not_clipped(point, clipping_plane);
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// First, check if the point pt is laying between planes defined by first_center and second_center.
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// Then check if it is inside the cylinder between first_center and second_center.
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const Vec3f centers_diff = this->second_center - this->first_center;
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if (first_center_diff.dot(centers_diff) <= 0.f && second_center_diff.dot(centers_diff) >= 0.f && (first_center_diff.cross(centers_diff).norm() / centers_diff.norm()) <= this->radius)
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return is_mesh_point_not_clipped(point, clipping_plane);
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return false;
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}
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// Is a point (in mesh coords) inside a Capsule2D cursor?
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bool TriangleSelector::Capsule2D::is_mesh_point_inside(const Vec3f &point) const
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{
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const Vec3f transformed_point = uniform_scaling ? point : Vec3f(trafo * point);
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const Vec3f first_center_diff = this->first_center - transformed_point;
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const Vec3f first_center_diff_projected = first_center_diff - first_center_diff.dot(this->dir) * this->dir;
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if (first_center_diff_projected.squaredNorm() < this->radius_sqr)
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return is_mesh_point_not_clipped(point, clipping_plane);
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const Vec3f second_center_diff = this->second_center - transformed_point;
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const Vec3f second_center_diff_projected = second_center_diff - second_center_diff.dot(this->dir) * this->dir;
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if (second_center_diff_projected.squaredNorm() < this->radius_sqr)
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return is_mesh_point_not_clipped(point, clipping_plane);
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const Vec3f centers_diff = this->second_center - this->first_center;
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const Vec3f centers_diff_projected = centers_diff - centers_diff.dot(this->dir) * this->dir;
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// First, check if the point is laying between first_center and second_center.
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if (first_center_diff_projected.dot(centers_diff_projected) <= 0.f && second_center_diff_projected.dot(centers_diff_projected) >= 0.f) {
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// Vector in the direction of line |AD| of the rectangle that intersects the circle with the center in first_center.
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const Vec3f rectangle_da_dir = centers_diff.cross(this->dir);
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// Vector pointing from first_center to the point 'A' of the rectangle.
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const Vec3f first_center_rectangle_a_diff = rectangle_da_dir.normalized() * this->radius;
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const Vec3f rectangle_a = this->first_center - first_center_rectangle_a_diff;
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const Vec3f rectangle_d = this->first_center + first_center_rectangle_a_diff;
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// Now check if the point is laying inside the rectangle between circles with centers in first_center and second_center.
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if ((rectangle_a - transformed_point).dot(rectangle_da_dir) <= 0.f && (rectangle_d - transformed_point).dot(rectangle_da_dir) >= 0.f)
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return is_mesh_point_not_clipped(point, clipping_plane);
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}
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return false;
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}
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// p1, p2, p3 are in mesh coords!
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@ -1754,4 +1946,102 @@ bool TriangleSelector::SinglePointCursor::is_pointer_in_triangle(const Vec3f &p1
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return is_circle_pointer_inside_triangle(p1_, p2_, p3_, center, dir, uniform_scaling, trafo);
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}
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// p1, p2, p3 are in mesh coords!
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bool TriangleSelector::DoublePointCursor::is_pointer_in_triangle(const Vec3f &p1_, const Vec3f &p2_, const Vec3f &p3_) const
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{
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return is_circle_pointer_inside_triangle(p1_, p2_, p3_, first_center, dir, uniform_scaling, trafo) ||
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is_circle_pointer_inside_triangle(p1_, p2_, p3_, second_center, dir, uniform_scaling, trafo);
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}
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bool line_plane_intersection(const Vec3f &line_a, const Vec3f &line_b, const Vec3f &plane_origin, const Vec3f &plane_normal, Vec3f &out_intersection)
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{
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Vec3f line_dir = line_b - line_a;
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float t_denominator = plane_normal.dot(line_dir);
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if (t_denominator == 0.f)
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return false;
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// Compute 'd' in plane equation by using some point (origin) on the plane
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float plane_d = plane_normal.dot(plane_origin);
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if (float t = (plane_d - plane_normal.dot(line_a)) / t_denominator; t >= 0.f && t <= 1.f) {
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out_intersection = line_a + t * line_dir;
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return true;
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}
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return false;
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}
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bool TriangleSelector::Capsule3D::is_edge_inside_cursor(const Triangle &tr, const std::vector<Vertex> &vertices) const
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{
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std::array<Vec3f, 3> pts;
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for (int i = 0; i < 3; ++i) {
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pts[i] = vertices[tr.verts_idxs[i]].v;
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if (!this->uniform_scaling)
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pts[i] = this->trafo * pts[i];
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}
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for (int side = 0; side < 3; ++side) {
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const Vec3f &edge_a = pts[side];
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const Vec3f &edge_b = pts[side < 2 ? side + 1 : 0];
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if (test_line_inside_capsule(edge_a, edge_b, this->first_center, this->second_center, this->radius))
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return true;
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}
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return false;
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}
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// Is edge inside cursor?
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bool TriangleSelector::Capsule2D::is_edge_inside_cursor(const Triangle &tr, const std::vector<Vertex> &vertices) const
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{
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std::array<Vec3f, 3> pts;
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for (int i = 0; i < 3; ++i) {
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pts[i] = vertices[tr.verts_idxs[i]].v;
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if (!this->uniform_scaling)
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pts[i] = this->trafo * pts[i];
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}
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const Vec3f centers_diff = this->second_center - this->first_center;
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// Vector in the direction of line |AD| of the rectangle that intersects the circle with the center in first_center.
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const Vec3f rectangle_da_dir = centers_diff.cross(this->dir);
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// Vector pointing from first_center to the point 'A' of the rectangle.
|
||||
const Vec3f first_center_rectangle_a_diff = rectangle_da_dir.normalized() * this->radius;
|
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const Vec3f rectangle_a = this->first_center - first_center_rectangle_a_diff;
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const Vec3f rectangle_d = this->first_center + first_center_rectangle_a_diff;
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auto edge_inside_rectangle = [&self = std::as_const(*this), ¢ers_diff](const Vec3f &edge_a, const Vec3f &edge_b, const Vec3f &plane_origin, const Vec3f &plane_normal) -> bool {
|
||||
Vec3f intersection(-1.f, -1.f, -1.f);
|
||||
if (line_plane_intersection(edge_a, edge_b, plane_origin, plane_normal, intersection)) {
|
||||
// Now check if the intersection point is inside the rectangle. That means it is between 'first_center' and 'second_center', resp. between 'A' and 'B'.
|
||||
if (self.first_center.dot(centers_diff) <= intersection.dot(centers_diff) && intersection.dot(centers_diff) <= self.second_center.dot(centers_diff))
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
};
|
||||
|
||||
for (int side = 0; side < 3; ++side) {
|
||||
const Vec3f &edge_a = pts[side];
|
||||
const Vec3f &edge_b = pts[side < 2 ? side + 1 : 0];
|
||||
const Vec3f edge_dir = edge_b - edge_a;
|
||||
const Vec3f edge_dir_n = edge_dir.normalized();
|
||||
|
||||
float t1 = (this->first_center - edge_a).dot(edge_dir_n);
|
||||
float t2 = (this->second_center - edge_a).dot(edge_dir_n);
|
||||
Vec3f vector1 = edge_a + t1 * edge_dir_n - this->first_center;
|
||||
Vec3f vector2 = edge_a + t2 * edge_dir_n - this->second_center;
|
||||
|
||||
// Vectors vector1 and vector2 are 3D vector from centers to the intersections. What we want to
|
||||
// measure is length of its projection onto plane perpendicular to dir.
|
||||
if (float dist = vector1.squaredNorm() - std::pow(vector1.dot(this->dir), 2.f); dist < this->radius_sqr && t1 >= 0.f && t1 <= edge_dir.norm())
|
||||
return true;
|
||||
|
||||
if (float dist = vector2.squaredNorm() - std::pow(vector2.dot(this->dir), 2.f); dist < this->radius_sqr && t2 >= 0.f && t2 <= edge_dir.norm())
|
||||
return true;
|
||||
|
||||
// Check if the edge is passing through the rectangle between first_center and second_center.
|
||||
if (edge_inside_rectangle(edge_a, edge_b, rectangle_a, (rectangle_d - rectangle_a)) || edge_inside_rectangle(edge_a, edge_b, rectangle_d, (rectangle_a - rectangle_d)))
|
||||
return true;
|
||||
}
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
} // namespace Slic3r
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue