diff options
Diffstat (limited to 'core/math')
-rw-r--r-- | core/math/math_2d.cpp | 299 | ||||
-rw-r--r-- | core/math/math_2d.h | 520 | ||||
-rw-r--r-- | core/math/rect2.cpp | 240 | ||||
-rw-r--r-- | core/math/rect2.h | 236 | ||||
-rw-r--r-- | core/math/transform_2d.cpp | 272 | ||||
-rw-r--r-- | core/math/transform_2d.h | 201 |
6 files changed, 950 insertions, 818 deletions
diff --git a/core/math/math_2d.cpp b/core/math/math_2d.cpp index 7fa75cfc3a..eccf0552b6 100644 --- a/core/math/math_2d.cpp +++ b/core/math/math_2d.cpp @@ -30,64 +30,6 @@ #include "math_2d.h" -bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const { - - real_t min = 0, max = 1; - int axis = 0; - real_t sign = 0; - - for (int i = 0; i < 2; i++) { - real_t seg_from = p_from[i]; - real_t seg_to = p_to[i]; - real_t box_begin = position[i]; - real_t box_end = box_begin + size[i]; - real_t cmin, cmax; - real_t csign; - - if (seg_from < seg_to) { - - if (seg_from > box_end || seg_to < box_begin) - return false; - real_t length = seg_to - seg_from; - cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0; - cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1; - csign = -1.0; - - } else { - - if (seg_to > box_end || seg_from < box_begin) - return false; - real_t length = seg_to - seg_from; - cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0; - cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1; - csign = 1.0; - } - - if (cmin > min) { - min = cmin; - axis = i; - sign = csign; - } - if (cmax < max) - max = cmax; - if (max < min) - return false; - } - - Vector2 rel = p_to - p_from; - - if (r_normal) { - Vector2 normal; - normal[axis] = sign; - *r_normal = normal; - } - - if (r_pos) - *r_pos = p_from + rel * min; - - return true; -} - /* Point2i */ Point2i Point2i::operator+(const Point2i &p_v) const { @@ -153,244 +95,3 @@ bool Point2i::operator!=(const Point2i &p_vec2) const { return x != p_vec2.x || y != p_vec2.y; } - -void Transform2D::invert() { - // FIXME: this function assumes the basis is a rotation matrix, with no scaling. - // Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that. - SWAP(elements[0][1], elements[1][0]); - elements[2] = basis_xform(-elements[2]); -} - -Transform2D Transform2D::inverse() const { - - Transform2D inv = *this; - inv.invert(); - return inv; -} - -void Transform2D::affine_invert() { - - real_t det = basis_determinant(); -#ifdef MATH_CHECKS - ERR_FAIL_COND(det == 0); -#endif - real_t idet = 1.0 / det; - - SWAP(elements[0][0], elements[1][1]); - elements[0] *= Vector2(idet, -idet); - elements[1] *= Vector2(-idet, idet); - - elements[2] = basis_xform(-elements[2]); -} - -Transform2D Transform2D::affine_inverse() const { - - Transform2D inv = *this; - inv.affine_invert(); - return inv; -} - -void Transform2D::rotate(real_t p_phi) { - *this = Transform2D(p_phi, Vector2()) * (*this); -} - -real_t Transform2D::get_rotation() const { - real_t det = basis_determinant(); - Transform2D m = orthonormalized(); - if (det < 0) { - m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling. - } - return Math::atan2(m[0].y, m[0].x); -} - -void Transform2D::set_rotation(real_t p_rot) { - - real_t cr = Math::cos(p_rot); - real_t sr = Math::sin(p_rot); - elements[0][0] = cr; - elements[0][1] = sr; - elements[1][0] = -sr; - elements[1][1] = cr; -} - -Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) { - - real_t cr = Math::cos(p_rot); - real_t sr = Math::sin(p_rot); - elements[0][0] = cr; - elements[0][1] = sr; - elements[1][0] = -sr; - elements[1][1] = cr; - elements[2] = p_pos; -} - -Size2 Transform2D::get_scale() const { - real_t det_sign = basis_determinant() > 0 ? 1 : -1; - return Size2(elements[0].length(), det_sign * elements[1].length()); -} - -void Transform2D::scale(const Size2 &p_scale) { - scale_basis(p_scale); - elements[2] *= p_scale; -} -void Transform2D::scale_basis(const Size2 &p_scale) { - - elements[0][0] *= p_scale.x; - elements[0][1] *= p_scale.y; - elements[1][0] *= p_scale.x; - elements[1][1] *= p_scale.y; -} -void Transform2D::translate(real_t p_tx, real_t p_ty) { - - translate(Vector2(p_tx, p_ty)); -} -void Transform2D::translate(const Vector2 &p_translation) { - - elements[2] += basis_xform(p_translation); -} - -void Transform2D::orthonormalize() { - - // Gram-Schmidt Process - - Vector2 x = elements[0]; - Vector2 y = elements[1]; - - x.normalize(); - y = (y - x * (x.dot(y))); - y.normalize(); - - elements[0] = x; - elements[1] = y; -} -Transform2D Transform2D::orthonormalized() const { - - Transform2D on = *this; - on.orthonormalize(); - return on; -} - -bool Transform2D::operator==(const Transform2D &p_transform) const { - - for (int i = 0; i < 3; i++) { - if (elements[i] != p_transform.elements[i]) - return false; - } - - return true; -} - -bool Transform2D::operator!=(const Transform2D &p_transform) const { - - for (int i = 0; i < 3; i++) { - if (elements[i] != p_transform.elements[i]) - return true; - } - - return false; -} - -void Transform2D::operator*=(const Transform2D &p_transform) { - - elements[2] = xform(p_transform.elements[2]); - - real_t x0, x1, y0, y1; - - x0 = tdotx(p_transform.elements[0]); - x1 = tdoty(p_transform.elements[0]); - y0 = tdotx(p_transform.elements[1]); - y1 = tdoty(p_transform.elements[1]); - - elements[0][0] = x0; - elements[0][1] = x1; - elements[1][0] = y0; - elements[1][1] = y1; -} - -Transform2D Transform2D::operator*(const Transform2D &p_transform) const { - - Transform2D t = *this; - t *= p_transform; - return t; -} - -Transform2D Transform2D::scaled(const Size2 &p_scale) const { - - Transform2D copy = *this; - copy.scale(p_scale); - return copy; -} - -Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const { - - Transform2D copy = *this; - copy.scale_basis(p_scale); - return copy; -} - -Transform2D Transform2D::untranslated() const { - - Transform2D copy = *this; - copy.elements[2] = Vector2(); - return copy; -} - -Transform2D Transform2D::translated(const Vector2 &p_offset) const { - - Transform2D copy = *this; - copy.translate(p_offset); - return copy; -} - -Transform2D Transform2D::rotated(real_t p_phi) const { - - Transform2D copy = *this; - copy.rotate(p_phi); - return copy; -} - -real_t Transform2D::basis_determinant() const { - - return elements[0].x * elements[1].y - elements[0].y * elements[1].x; -} - -Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_c) const { - - //extract parameters - Vector2 p1 = get_origin(); - Vector2 p2 = p_transform.get_origin(); - - real_t r1 = get_rotation(); - real_t r2 = p_transform.get_rotation(); - - Size2 s1 = get_scale(); - Size2 s2 = p_transform.get_scale(); - - //slerp rotation - Vector2 v1(Math::cos(r1), Math::sin(r1)); - Vector2 v2(Math::cos(r2), Math::sin(r2)); - - real_t dot = v1.dot(v2); - - dot = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1] - - Vector2 v; - - if (dot > 0.9995) { - v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues - } else { - real_t angle = p_c * Math::acos(dot); - Vector2 v3 = (v2 - v1 * dot).normalized(); - v = v1 * Math::cos(angle) + v3 * Math::sin(angle); - } - - //construct matrix - Transform2D res(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c)); - res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c)); - return res; -} - -Transform2D::operator String() const { - - return String(String() + elements[0] + ", " + elements[1] + ", " + elements[2]); -} diff --git a/core/math/math_2d.h b/core/math/math_2d.h index a764e3e3cf..e5edb08a1f 100644 --- a/core/math/math_2d.h +++ b/core/math/math_2d.h @@ -31,212 +31,10 @@ #ifndef MATH_2D_H #define MATH_2D_H -#include "math_funcs.h" -#include "ustring.h" -#include "vector2.h" +#include "transform_2d.h" /** @author Juan Linietsky <reduzio@gmail.com> */ -struct Transform2D; - -struct Rect2 { - - Point2 position; - Size2 size; - - const Vector2 &get_position() const { return position; } - void set_position(const Vector2 &p_pos) { position = p_pos; } - const Vector2 &get_size() const { return size; } - void set_size(const Vector2 &p_size) { size = p_size; } - - real_t get_area() const { return size.width * size.height; } - - inline bool intersects(const Rect2 &p_rect) const { - if (position.x >= (p_rect.position.x + p_rect.size.width)) - return false; - if ((position.x + size.width) <= p_rect.position.x) - return false; - if (position.y >= (p_rect.position.y + p_rect.size.height)) - return false; - if ((position.y + size.height) <= p_rect.position.y) - return false; - - return true; - } - - inline real_t distance_to(const Vector2 &p_point) const { - - real_t dist = 0.0; - bool inside = true; - - if (p_point.x < position.x) { - real_t d = position.x - p_point.x; - dist = inside ? d : MIN(dist, d); - inside = false; - } - if (p_point.y < position.y) { - real_t d = position.y - p_point.y; - dist = inside ? d : MIN(dist, d); - inside = false; - } - if (p_point.x >= (position.x + size.x)) { - real_t d = p_point.x - (position.x + size.x); - dist = inside ? d : MIN(dist, d); - inside = false; - } - if (p_point.y >= (position.y + size.y)) { - real_t d = p_point.y - (position.y + size.y); - dist = inside ? d : MIN(dist, d); - inside = false; - } - - if (inside) - return 0; - else - return dist; - } - - _FORCE_INLINE_ bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const; - - bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = NULL, Point2 *r_normal = NULL) const; - - inline bool encloses(const Rect2 &p_rect) const { - - return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) && - ((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) && - ((p_rect.position.y + p_rect.size.y) < (position.y + size.y)); - } - - inline bool has_no_area() const { - - return (size.x <= 0 || size.y <= 0); - } - inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect - - Rect2 new_rect = p_rect; - - if (!intersects(new_rect)) - return Rect2(); - - new_rect.position.x = MAX(p_rect.position.x, position.x); - new_rect.position.y = MAX(p_rect.position.y, position.y); - - Point2 p_rect_end = p_rect.position + p_rect.size; - Point2 end = position + size; - - new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x; - new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y; - - return new_rect; - } - - inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect - - Rect2 new_rect; - - new_rect.position.x = MIN(p_rect.position.x, position.x); - new_rect.position.y = MIN(p_rect.position.y, position.y); - - new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x); - new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y); - - new_rect.size = new_rect.size - new_rect.position; //make relative again - - return new_rect; - }; - inline bool has_point(const Point2 &p_point) const { - if (p_point.x < position.x) - return false; - if (p_point.y < position.y) - return false; - - if (p_point.x >= (position.x + size.x)) - return false; - if (p_point.y >= (position.y + size.y)) - return false; - - return true; - } - - inline bool no_area() const { return (size.width <= 0 || size.height <= 0); } - - bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; } - bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; } - - inline Rect2 grow(real_t p_by) const { - - Rect2 g = *this; - g.position.x -= p_by; - g.position.y -= p_by; - g.size.width += p_by * 2; - g.size.height += p_by * 2; - return g; - } - - inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const { - Rect2 g = *this; - g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0, - (MARGIN_TOP == p_margin) ? p_amount : 0, - (MARGIN_RIGHT == p_margin) ? p_amount : 0, - (MARGIN_BOTTOM == p_margin) ? p_amount : 0); - return g; - } - - inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const { - - Rect2 g = *this; - g.position.x -= p_left; - g.position.y -= p_top; - g.size.width += p_left + p_right; - g.size.height += p_top + p_bottom; - - return g; - } - - inline Rect2 expand(const Vector2 &p_vector) const { - - Rect2 r = *this; - r.expand_to(p_vector); - return r; - } - - inline void expand_to(const Vector2 &p_vector) { //in place function for speed - - Vector2 begin = position; - Vector2 end = position + size; - - if (p_vector.x < begin.x) - begin.x = p_vector.x; - if (p_vector.y < begin.y) - begin.y = p_vector.y; - - if (p_vector.x > end.x) - end.x = p_vector.x; - if (p_vector.y > end.y) - end.y = p_vector.y; - - position = begin; - size = end - begin; - } - - inline Rect2 abs() const { - - return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs()); - } - - operator String() const { return String(position) + ", " + String(size); } - - Rect2() {} - Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) : - position(Point2(p_x, p_y)), - size(Size2(p_width, p_height)) { - } - Rect2(const Point2 &p_pos, const Size2 &p_size) : - position(p_pos), - size(p_size) { - } -}; - /* INTEGER STUFF */ struct Point2i { @@ -435,320 +233,4 @@ struct Rect2i { } }; -struct Transform2D { - // Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper": - // M = (elements[0][0] elements[1][0]) - // (elements[0][1] elements[1][1]) - // This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i]. - // Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here. - // This requires additional care when working with explicit indices. - // See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading. - - // Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down, - // and angle is measure from +X to +Y in a clockwise-fashion. - - Vector2 elements[3]; - - _FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; } - _FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; } - - const Vector2 &operator[](int p_idx) const { return elements[p_idx]; } - Vector2 &operator[](int p_idx) { return elements[p_idx]; } - - _FORCE_INLINE_ Vector2 get_axis(int p_axis) const { - ERR_FAIL_INDEX_V(p_axis, 3, Vector2()); - return elements[p_axis]; - } - _FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) { - ERR_FAIL_INDEX(p_axis, 3); - elements[p_axis] = p_vec; - } - - void invert(); - Transform2D inverse() const; - - void affine_invert(); - Transform2D affine_inverse() const; - - void set_rotation(real_t p_rot); - real_t get_rotation() const; - _FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale); - void rotate(real_t p_phi); - - void scale(const Size2 &p_scale); - void scale_basis(const Size2 &p_scale); - void translate(real_t p_tx, real_t p_ty); - void translate(const Vector2 &p_translation); - - real_t basis_determinant() const; - - Size2 get_scale() const; - - _FORCE_INLINE_ const Vector2 &get_origin() const { return elements[2]; } - _FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; } - - Transform2D scaled(const Size2 &p_scale) const; - Transform2D basis_scaled(const Size2 &p_scale) const; - Transform2D translated(const Vector2 &p_offset) const; - Transform2D rotated(real_t p_phi) const; - - Transform2D untranslated() const; - - void orthonormalize(); - Transform2D orthonormalized() const; - - bool operator==(const Transform2D &p_transform) const; - bool operator!=(const Transform2D &p_transform) const; - - void operator*=(const Transform2D &p_transform); - Transform2D operator*(const Transform2D &p_transform) const; - - Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const; - - _FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const; - _FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const; - _FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const; - _FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const; - _FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const; - _FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const; - - operator String() const; - - Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) { - - elements[0][0] = xx; - elements[0][1] = xy; - elements[1][0] = yx; - elements[1][1] = yy; - elements[2][0] = ox; - elements[2][1] = oy; - } - - Transform2D(real_t p_rot, const Vector2 &p_pos); - Transform2D() { - elements[0][0] = 1.0; - elements[1][1] = 1.0; - } -}; - -bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const { - - //SAT intersection between local and transformed rect2 - - Vector2 xf_points[4] = { - p_xform.xform(p_rect.position), - p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)), - p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)), - p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)), - }; - - real_t low_limit; - - //base rect2 first (faster) - - if (xf_points[0].y > position.y) - goto next1; - if (xf_points[1].y > position.y) - goto next1; - if (xf_points[2].y > position.y) - goto next1; - if (xf_points[3].y > position.y) - goto next1; - - return false; - -next1: - - low_limit = position.y + size.y; - - if (xf_points[0].y < low_limit) - goto next2; - if (xf_points[1].y < low_limit) - goto next2; - if (xf_points[2].y < low_limit) - goto next2; - if (xf_points[3].y < low_limit) - goto next2; - - return false; - -next2: - - if (xf_points[0].x > position.x) - goto next3; - if (xf_points[1].x > position.x) - goto next3; - if (xf_points[2].x > position.x) - goto next3; - if (xf_points[3].x > position.x) - goto next3; - - return false; - -next3: - - low_limit = position.x + size.x; - - if (xf_points[0].x < low_limit) - goto next4; - if (xf_points[1].x < low_limit) - goto next4; - if (xf_points[2].x < low_limit) - goto next4; - if (xf_points[3].x < low_limit) - goto next4; - - return false; - -next4: - - Vector2 xf_points2[4] = { - position, - Vector2(position.x + size.x, position.y), - Vector2(position.x, position.y + size.y), - Vector2(position.x + size.x, position.y + size.y), - }; - - real_t maxa = p_xform.elements[0].dot(xf_points2[0]); - real_t mina = maxa; - - real_t dp = p_xform.elements[0].dot(xf_points2[1]); - maxa = MAX(dp, maxa); - mina = MIN(dp, mina); - - dp = p_xform.elements[0].dot(xf_points2[2]); - maxa = MAX(dp, maxa); - mina = MIN(dp, mina); - - dp = p_xform.elements[0].dot(xf_points2[3]); - maxa = MAX(dp, maxa); - mina = MIN(dp, mina); - - real_t maxb = p_xform.elements[0].dot(xf_points[0]); - real_t minb = maxb; - - dp = p_xform.elements[0].dot(xf_points[1]); - maxb = MAX(dp, maxb); - minb = MIN(dp, minb); - - dp = p_xform.elements[0].dot(xf_points[2]); - maxb = MAX(dp, maxb); - minb = MIN(dp, minb); - - dp = p_xform.elements[0].dot(xf_points[3]); - maxb = MAX(dp, maxb); - minb = MIN(dp, minb); - - if (mina > maxb) - return false; - if (minb > maxa) - return false; - - maxa = p_xform.elements[1].dot(xf_points2[0]); - mina = maxa; - - dp = p_xform.elements[1].dot(xf_points2[1]); - maxa = MAX(dp, maxa); - mina = MIN(dp, mina); - - dp = p_xform.elements[1].dot(xf_points2[2]); - maxa = MAX(dp, maxa); - mina = MIN(dp, mina); - - dp = p_xform.elements[1].dot(xf_points2[3]); - maxa = MAX(dp, maxa); - mina = MIN(dp, mina); - - maxb = p_xform.elements[1].dot(xf_points[0]); - minb = maxb; - - dp = p_xform.elements[1].dot(xf_points[1]); - maxb = MAX(dp, maxb); - minb = MIN(dp, minb); - - dp = p_xform.elements[1].dot(xf_points[2]); - maxb = MAX(dp, maxb); - minb = MIN(dp, minb); - - dp = p_xform.elements[1].dot(xf_points[3]); - maxb = MAX(dp, maxb); - minb = MIN(dp, minb); - - if (mina > maxb) - return false; - if (minb > maxa) - return false; - - return true; -} - -Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const { - - return Vector2( - tdotx(p_vec), - tdoty(p_vec)); -} - -Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const { - - return Vector2( - elements[0].dot(p_vec), - elements[1].dot(p_vec)); -} - -Vector2 Transform2D::xform(const Vector2 &p_vec) const { - - return Vector2( - tdotx(p_vec), - tdoty(p_vec)) + - elements[2]; -} -Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const { - - Vector2 v = p_vec - elements[2]; - - return Vector2( - elements[0].dot(v), - elements[1].dot(v)); -} -Rect2 Transform2D::xform(const Rect2 &p_rect) const { - - Vector2 x = elements[0] * p_rect.size.x; - Vector2 y = elements[1] * p_rect.size.y; - Vector2 pos = xform(p_rect.position); - - Rect2 new_rect; - new_rect.position = pos; - new_rect.expand_to(pos + x); - new_rect.expand_to(pos + y); - new_rect.expand_to(pos + x + y); - return new_rect; -} - -void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) { - - elements[0][0] = Math::cos(p_rot) * p_scale.x; - elements[1][1] = Math::cos(p_rot) * p_scale.y; - elements[1][0] = -Math::sin(p_rot) * p_scale.y; - elements[0][1] = Math::sin(p_rot) * p_scale.x; -} - -Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const { - - Vector2 ends[4] = { - xform_inv(p_rect.position), - xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)), - xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)), - xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)) - }; - - Rect2 new_rect; - new_rect.position = ends[0]; - new_rect.expand_to(ends[1]); - new_rect.expand_to(ends[2]); - new_rect.expand_to(ends[3]); - - return new_rect; -} - #endif diff --git a/core/math/rect2.cpp b/core/math/rect2.cpp new file mode 100644 index 0000000000..480bccdff1 --- /dev/null +++ b/core/math/rect2.cpp @@ -0,0 +1,240 @@ +/*************************************************************************/ +/* rect2.cpp */ +/*************************************************************************/ +/* This file is part of: */ +/* GODOT ENGINE */ +/* https://godotengine.org */ +/*************************************************************************/ +/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */ +/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */ +/* */ +/* Permission is hereby granted, free of charge, to any person obtaining */ +/* a copy of this software and associated documentation files (the */ +/* "Software"), to deal in the Software without restriction, including */ +/* without limitation the rights to use, copy, modify, merge, publish, */ +/* distribute, sublicense, and/or sell copies of the Software, and to */ +/* permit persons to whom the Software is furnished to do so, subject to */ +/* the following conditions: */ +/* */ +/* The above copyright notice and this permission notice shall be */ +/* included in all copies or substantial portions of the Software. */ +/* */ +/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ +/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ +/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/ +/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ +/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ +/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ +/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ +/*************************************************************************/ + +#include "transform_2d.h" // Includes rect2.h but Rect2 needs Transform2D + +bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const { + + real_t min = 0, max = 1; + int axis = 0; + real_t sign = 0; + + for (int i = 0; i < 2; i++) { + real_t seg_from = p_from[i]; + real_t seg_to = p_to[i]; + real_t box_begin = position[i]; + real_t box_end = box_begin + size[i]; + real_t cmin, cmax; + real_t csign; + + if (seg_from < seg_to) { + + if (seg_from > box_end || seg_to < box_begin) + return false; + real_t length = seg_to - seg_from; + cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0; + cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1; + csign = -1.0; + + } else { + + if (seg_to > box_end || seg_from < box_begin) + return false; + real_t length = seg_to - seg_from; + cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0; + cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1; + csign = 1.0; + } + + if (cmin > min) { + min = cmin; + axis = i; + sign = csign; + } + if (cmax < max) + max = cmax; + if (max < min) + return false; + } + + Vector2 rel = p_to - p_from; + + if (r_normal) { + Vector2 normal; + normal[axis] = sign; + *r_normal = normal; + } + + if (r_pos) + *r_pos = p_from + rel * min; + + return true; +} + +bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const { + + //SAT intersection between local and transformed rect2 + + Vector2 xf_points[4] = { + p_xform.xform(p_rect.position), + p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)), + p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)), + p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)), + }; + + real_t low_limit; + + //base rect2 first (faster) + + if (xf_points[0].y > position.y) + goto next1; + if (xf_points[1].y > position.y) + goto next1; + if (xf_points[2].y > position.y) + goto next1; + if (xf_points[3].y > position.y) + goto next1; + + return false; + +next1: + + low_limit = position.y + size.y; + + if (xf_points[0].y < low_limit) + goto next2; + if (xf_points[1].y < low_limit) + goto next2; + if (xf_points[2].y < low_limit) + goto next2; + if (xf_points[3].y < low_limit) + goto next2; + + return false; + +next2: + + if (xf_points[0].x > position.x) + goto next3; + if (xf_points[1].x > position.x) + goto next3; + if (xf_points[2].x > position.x) + goto next3; + if (xf_points[3].x > position.x) + goto next3; + + return false; + +next3: + + low_limit = position.x + size.x; + + if (xf_points[0].x < low_limit) + goto next4; + if (xf_points[1].x < low_limit) + goto next4; + if (xf_points[2].x < low_limit) + goto next4; + if (xf_points[3].x < low_limit) + goto next4; + + return false; + +next4: + + Vector2 xf_points2[4] = { + position, + Vector2(position.x + size.x, position.y), + Vector2(position.x, position.y + size.y), + Vector2(position.x + size.x, position.y + size.y), + }; + + real_t maxa = p_xform.elements[0].dot(xf_points2[0]); + real_t mina = maxa; + + real_t dp = p_xform.elements[0].dot(xf_points2[1]); + maxa = MAX(dp, maxa); + mina = MIN(dp, mina); + + dp = p_xform.elements[0].dot(xf_points2[2]); + maxa = MAX(dp, maxa); + mina = MIN(dp, mina); + + dp = p_xform.elements[0].dot(xf_points2[3]); + maxa = MAX(dp, maxa); + mina = MIN(dp, mina); + + real_t maxb = p_xform.elements[0].dot(xf_points[0]); + real_t minb = maxb; + + dp = p_xform.elements[0].dot(xf_points[1]); + maxb = MAX(dp, maxb); + minb = MIN(dp, minb); + + dp = p_xform.elements[0].dot(xf_points[2]); + maxb = MAX(dp, maxb); + minb = MIN(dp, minb); + + dp = p_xform.elements[0].dot(xf_points[3]); + maxb = MAX(dp, maxb); + minb = MIN(dp, minb); + + if (mina > maxb) + return false; + if (minb > maxa) + return false; + + maxa = p_xform.elements[1].dot(xf_points2[0]); + mina = maxa; + + dp = p_xform.elements[1].dot(xf_points2[1]); + maxa = MAX(dp, maxa); + mina = MIN(dp, mina); + + dp = p_xform.elements[1].dot(xf_points2[2]); + maxa = MAX(dp, maxa); + mina = MIN(dp, mina); + + dp = p_xform.elements[1].dot(xf_points2[3]); + maxa = MAX(dp, maxa); + mina = MIN(dp, mina); + + maxb = p_xform.elements[1].dot(xf_points[0]); + minb = maxb; + + dp = p_xform.elements[1].dot(xf_points[1]); + maxb = MAX(dp, maxb); + minb = MIN(dp, minb); + + dp = p_xform.elements[1].dot(xf_points[2]); + maxb = MAX(dp, maxb); + minb = MIN(dp, minb); + + dp = p_xform.elements[1].dot(xf_points[3]); + maxb = MAX(dp, maxb); + minb = MIN(dp, minb); + + if (mina > maxb) + return false; + if (minb > maxa) + return false; + + return true; +} diff --git a/core/math/rect2.h b/core/math/rect2.h new file mode 100644 index 0000000000..d156618be6 --- /dev/null +++ b/core/math/rect2.h @@ -0,0 +1,236 @@ +/*************************************************************************/ +/* rect2.h */ +/*************************************************************************/ +/* This file is part of: */ +/* GODOT ENGINE */ +/* https://godotengine.org */ +/*************************************************************************/ +/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */ +/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */ +/* */ +/* Permission is hereby granted, free of charge, to any person obtaining */ +/* a copy of this software and associated documentation files (the */ +/* "Software"), to deal in the Software without restriction, including */ +/* without limitation the rights to use, copy, modify, merge, publish, */ +/* distribute, sublicense, and/or sell copies of the Software, and to */ +/* permit persons to whom the Software is furnished to do so, subject to */ +/* the following conditions: */ +/* */ +/* The above copyright notice and this permission notice shall be */ +/* included in all copies or substantial portions of the Software. */ +/* */ +/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ +/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ +/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/ +/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ +/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ +/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ +/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ +/*************************************************************************/ + +#ifndef RECT2_H +#define RECT2_H + +#include "vector2.h" // also includes math_funcs and ustring + +struct Transform2D; + +struct Rect2 { + + Point2 position; + Size2 size; + + const Vector2 &get_position() const { return position; } + void set_position(const Vector2 &p_pos) { position = p_pos; } + const Vector2 &get_size() const { return size; } + void set_size(const Vector2 &p_size) { size = p_size; } + + real_t get_area() const { return size.width * size.height; } + + inline bool intersects(const Rect2 &p_rect) const { + if (position.x >= (p_rect.position.x + p_rect.size.width)) + return false; + if ((position.x + size.width) <= p_rect.position.x) + return false; + if (position.y >= (p_rect.position.y + p_rect.size.height)) + return false; + if ((position.y + size.height) <= p_rect.position.y) + return false; + + return true; + } + + inline real_t distance_to(const Vector2 &p_point) const { + + real_t dist = 0.0; + bool inside = true; + + if (p_point.x < position.x) { + real_t d = position.x - p_point.x; + dist = inside ? d : MIN(dist, d); + inside = false; + } + if (p_point.y < position.y) { + real_t d = position.y - p_point.y; + dist = inside ? d : MIN(dist, d); + inside = false; + } + if (p_point.x >= (position.x + size.x)) { + real_t d = p_point.x - (position.x + size.x); + dist = inside ? d : MIN(dist, d); + inside = false; + } + if (p_point.y >= (position.y + size.y)) { + real_t d = p_point.y - (position.y + size.y); + dist = inside ? d : MIN(dist, d); + inside = false; + } + + if (inside) + return 0; + else + return dist; + } + + bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const; + + bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = NULL, Point2 *r_normal = NULL) const; + + inline bool encloses(const Rect2 &p_rect) const { + + return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) && + ((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) && + ((p_rect.position.y + p_rect.size.y) < (position.y + size.y)); + } + + inline bool has_no_area() const { + + return (size.x <= 0 || size.y <= 0); + } + inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect + + Rect2 new_rect = p_rect; + + if (!intersects(new_rect)) + return Rect2(); + + new_rect.position.x = MAX(p_rect.position.x, position.x); + new_rect.position.y = MAX(p_rect.position.y, position.y); + + Point2 p_rect_end = p_rect.position + p_rect.size; + Point2 end = position + size; + + new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x; + new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y; + + return new_rect; + } + + inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect + + Rect2 new_rect; + + new_rect.position.x = MIN(p_rect.position.x, position.x); + new_rect.position.y = MIN(p_rect.position.y, position.y); + + new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x); + new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y); + + new_rect.size = new_rect.size - new_rect.position; //make relative again + + return new_rect; + }; + inline bool has_point(const Point2 &p_point) const { + if (p_point.x < position.x) + return false; + if (p_point.y < position.y) + return false; + + if (p_point.x >= (position.x + size.x)) + return false; + if (p_point.y >= (position.y + size.y)) + return false; + + return true; + } + + inline bool no_area() const { return (size.width <= 0 || size.height <= 0); } + + bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; } + bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; } + + inline Rect2 grow(real_t p_by) const { + + Rect2 g = *this; + g.position.x -= p_by; + g.position.y -= p_by; + g.size.width += p_by * 2; + g.size.height += p_by * 2; + return g; + } + + inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const { + Rect2 g = *this; + g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0, + (MARGIN_TOP == p_margin) ? p_amount : 0, + (MARGIN_RIGHT == p_margin) ? p_amount : 0, + (MARGIN_BOTTOM == p_margin) ? p_amount : 0); + return g; + } + + inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const { + + Rect2 g = *this; + g.position.x -= p_left; + g.position.y -= p_top; + g.size.width += p_left + p_right; + g.size.height += p_top + p_bottom; + + return g; + } + + inline Rect2 expand(const Vector2 &p_vector) const { + + Rect2 r = *this; + r.expand_to(p_vector); + return r; + } + + inline void expand_to(const Vector2 &p_vector) { //in place function for speed + + Vector2 begin = position; + Vector2 end = position + size; + + if (p_vector.x < begin.x) + begin.x = p_vector.x; + if (p_vector.y < begin.y) + begin.y = p_vector.y; + + if (p_vector.x > end.x) + end.x = p_vector.x; + if (p_vector.y > end.y) + end.y = p_vector.y; + + position = begin; + size = end - begin; + } + + inline Rect2 abs() const { + + return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs()); + } + + operator String() const { return String(position) + ", " + String(size); } + + Rect2() {} + Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) : + position(Point2(p_x, p_y)), + size(Size2(p_width, p_height)) { + } + Rect2(const Point2 &p_pos, const Size2 &p_size) : + position(p_pos), + size(p_size) { + } +}; + +#endif // RECT2_H diff --git a/core/math/transform_2d.cpp b/core/math/transform_2d.cpp new file mode 100644 index 0000000000..4bb763c879 --- /dev/null +++ b/core/math/transform_2d.cpp @@ -0,0 +1,272 @@ +/*************************************************************************/ +/* transform_2d.cpp */ +/*************************************************************************/ +/* This file is part of: */ +/* GODOT ENGINE */ +/* https://godotengine.org */ +/*************************************************************************/ +/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */ +/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */ +/* */ +/* Permission is hereby granted, free of charge, to any person obtaining */ +/* a copy of this software and associated documentation files (the */ +/* "Software"), to deal in the Software without restriction, including */ +/* without limitation the rights to use, copy, modify, merge, publish, */ +/* distribute, sublicense, and/or sell copies of the Software, and to */ +/* permit persons to whom the Software is furnished to do so, subject to */ +/* the following conditions: */ +/* */ +/* The above copyright notice and this permission notice shall be */ +/* included in all copies or substantial portions of the Software. */ +/* */ +/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ +/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ +/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/ +/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ +/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ +/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ +/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ +/*************************************************************************/ + +#include "transform_2d.h" + +void Transform2D::invert() { + // FIXME: this function assumes the basis is a rotation matrix, with no scaling. + // Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that. + SWAP(elements[0][1], elements[1][0]); + elements[2] = basis_xform(-elements[2]); +} + +Transform2D Transform2D::inverse() const { + + Transform2D inv = *this; + inv.invert(); + return inv; +} + +void Transform2D::affine_invert() { + + real_t det = basis_determinant(); +#ifdef MATH_CHECKS + ERR_FAIL_COND(det == 0); +#endif + real_t idet = 1.0 / det; + + SWAP(elements[0][0], elements[1][1]); + elements[0] *= Vector2(idet, -idet); + elements[1] *= Vector2(-idet, idet); + + elements[2] = basis_xform(-elements[2]); +} + +Transform2D Transform2D::affine_inverse() const { + + Transform2D inv = *this; + inv.affine_invert(); + return inv; +} + +void Transform2D::rotate(real_t p_phi) { + *this = Transform2D(p_phi, Vector2()) * (*this); +} + +real_t Transform2D::get_rotation() const { + real_t det = basis_determinant(); + Transform2D m = orthonormalized(); + if (det < 0) { + m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling. + } + return Math::atan2(m[0].y, m[0].x); +} + +void Transform2D::set_rotation(real_t p_rot) { + + real_t cr = Math::cos(p_rot); + real_t sr = Math::sin(p_rot); + elements[0][0] = cr; + elements[0][1] = sr; + elements[1][0] = -sr; + elements[1][1] = cr; +} + +Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) { + + real_t cr = Math::cos(p_rot); + real_t sr = Math::sin(p_rot); + elements[0][0] = cr; + elements[0][1] = sr; + elements[1][0] = -sr; + elements[1][1] = cr; + elements[2] = p_pos; +} + +Size2 Transform2D::get_scale() const { + real_t det_sign = basis_determinant() > 0 ? 1 : -1; + return Size2(elements[0].length(), det_sign * elements[1].length()); +} + +void Transform2D::scale(const Size2 &p_scale) { + scale_basis(p_scale); + elements[2] *= p_scale; +} +void Transform2D::scale_basis(const Size2 &p_scale) { + + elements[0][0] *= p_scale.x; + elements[0][1] *= p_scale.y; + elements[1][0] *= p_scale.x; + elements[1][1] *= p_scale.y; +} +void Transform2D::translate(real_t p_tx, real_t p_ty) { + + translate(Vector2(p_tx, p_ty)); +} +void Transform2D::translate(const Vector2 &p_translation) { + + elements[2] += basis_xform(p_translation); +} + +void Transform2D::orthonormalize() { + + // Gram-Schmidt Process + + Vector2 x = elements[0]; + Vector2 y = elements[1]; + + x.normalize(); + y = (y - x * (x.dot(y))); + y.normalize(); + + elements[0] = x; + elements[1] = y; +} +Transform2D Transform2D::orthonormalized() const { + + Transform2D on = *this; + on.orthonormalize(); + return on; +} + +bool Transform2D::operator==(const Transform2D &p_transform) const { + + for (int i = 0; i < 3; i++) { + if (elements[i] != p_transform.elements[i]) + return false; + } + + return true; +} + +bool Transform2D::operator!=(const Transform2D &p_transform) const { + + for (int i = 0; i < 3; i++) { + if (elements[i] != p_transform.elements[i]) + return true; + } + + return false; +} + +void Transform2D::operator*=(const Transform2D &p_transform) { + + elements[2] = xform(p_transform.elements[2]); + + real_t x0, x1, y0, y1; + + x0 = tdotx(p_transform.elements[0]); + x1 = tdoty(p_transform.elements[0]); + y0 = tdotx(p_transform.elements[1]); + y1 = tdoty(p_transform.elements[1]); + + elements[0][0] = x0; + elements[0][1] = x1; + elements[1][0] = y0; + elements[1][1] = y1; +} + +Transform2D Transform2D::operator*(const Transform2D &p_transform) const { + + Transform2D t = *this; + t *= p_transform; + return t; +} + +Transform2D Transform2D::scaled(const Size2 &p_scale) const { + + Transform2D copy = *this; + copy.scale(p_scale); + return copy; +} + +Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const { + + Transform2D copy = *this; + copy.scale_basis(p_scale); + return copy; +} + +Transform2D Transform2D::untranslated() const { + + Transform2D copy = *this; + copy.elements[2] = Vector2(); + return copy; +} + +Transform2D Transform2D::translated(const Vector2 &p_offset) const { + + Transform2D copy = *this; + copy.translate(p_offset); + return copy; +} + +Transform2D Transform2D::rotated(real_t p_phi) const { + + Transform2D copy = *this; + copy.rotate(p_phi); + return copy; +} + +real_t Transform2D::basis_determinant() const { + + return elements[0].x * elements[1].y - elements[0].y * elements[1].x; +} + +Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_c) const { + + //extract parameters + Vector2 p1 = get_origin(); + Vector2 p2 = p_transform.get_origin(); + + real_t r1 = get_rotation(); + real_t r2 = p_transform.get_rotation(); + + Size2 s1 = get_scale(); + Size2 s2 = p_transform.get_scale(); + + //slerp rotation + Vector2 v1(Math::cos(r1), Math::sin(r1)); + Vector2 v2(Math::cos(r2), Math::sin(r2)); + + real_t dot = v1.dot(v2); + + dot = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1] + + Vector2 v; + + if (dot > 0.9995) { + v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues + } else { + real_t angle = p_c * Math::acos(dot); + Vector2 v3 = (v2 - v1 * dot).normalized(); + v = v1 * Math::cos(angle) + v3 * Math::sin(angle); + } + + //construct matrix + Transform2D res(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c)); + res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c)); + return res; +} + +Transform2D::operator String() const { + + return String(String() + elements[0] + ", " + elements[1] + ", " + elements[2]); +} diff --git a/core/math/transform_2d.h b/core/math/transform_2d.h new file mode 100644 index 0000000000..bf73755f0d --- /dev/null +++ b/core/math/transform_2d.h @@ -0,0 +1,201 @@ +/*************************************************************************/ +/* transform_2d.h */ +/*************************************************************************/ +/* This file is part of: */ +/* GODOT ENGINE */ +/* https://godotengine.org */ +/*************************************************************************/ +/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */ +/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */ +/* */ +/* Permission is hereby granted, free of charge, to any person obtaining */ +/* a copy of this software and associated documentation files (the */ +/* "Software"), to deal in the Software without restriction, including */ +/* without limitation the rights to use, copy, modify, merge, publish, */ +/* distribute, sublicense, and/or sell copies of the Software, and to */ +/* permit persons to whom the Software is furnished to do so, subject to */ +/* the following conditions: */ +/* */ +/* The above copyright notice and this permission notice shall be */ +/* included in all copies or substantial portions of the Software. */ +/* */ +/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ +/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ +/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/ +/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ +/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ +/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ +/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ +/*************************************************************************/ + +#ifndef TRANSFORM_2D_H +#define TRANSFORM_2D_H + +#include "rect2.h" // also includes vector2, math_funcs, and ustring + +struct Transform2D { + // Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper": + // M = (elements[0][0] elements[1][0]) + // (elements[0][1] elements[1][1]) + // This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i]. + // Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here. + // This requires additional care when working with explicit indices. + // See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading. + + // Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down, + // and angle is measure from +X to +Y in a clockwise-fashion. + + Vector2 elements[3]; + + _FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; } + _FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; } + + const Vector2 &operator[](int p_idx) const { return elements[p_idx]; } + Vector2 &operator[](int p_idx) { return elements[p_idx]; } + + _FORCE_INLINE_ Vector2 get_axis(int p_axis) const { + ERR_FAIL_INDEX_V(p_axis, 3, Vector2()); + return elements[p_axis]; + } + _FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) { + ERR_FAIL_INDEX(p_axis, 3); + elements[p_axis] = p_vec; + } + + void invert(); + Transform2D inverse() const; + + void affine_invert(); + Transform2D affine_inverse() const; + + void set_rotation(real_t p_rot); + real_t get_rotation() const; + _FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale); + void rotate(real_t p_phi); + + void scale(const Size2 &p_scale); + void scale_basis(const Size2 &p_scale); + void translate(real_t p_tx, real_t p_ty); + void translate(const Vector2 &p_translation); + + real_t basis_determinant() const; + + Size2 get_scale() const; + + _FORCE_INLINE_ const Vector2 &get_origin() const { return elements[2]; } + _FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; } + + Transform2D scaled(const Size2 &p_scale) const; + Transform2D basis_scaled(const Size2 &p_scale) const; + Transform2D translated(const Vector2 &p_offset) const; + Transform2D rotated(real_t p_phi) const; + + Transform2D untranslated() const; + + void orthonormalize(); + Transform2D orthonormalized() const; + + bool operator==(const Transform2D &p_transform) const; + bool operator!=(const Transform2D &p_transform) const; + + void operator*=(const Transform2D &p_transform); + Transform2D operator*(const Transform2D &p_transform) const; + + Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const; + + _FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const; + _FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const; + _FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const; + _FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const; + _FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const; + _FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const; + + operator String() const; + + Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) { + + elements[0][0] = xx; + elements[0][1] = xy; + elements[1][0] = yx; + elements[1][1] = yy; + elements[2][0] = ox; + elements[2][1] = oy; + } + + Transform2D(real_t p_rot, const Vector2 &p_pos); + Transform2D() { + elements[0][0] = 1.0; + elements[1][1] = 1.0; + } +}; + +Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const { + + return Vector2( + tdotx(p_vec), + tdoty(p_vec)); +} + +Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const { + + return Vector2( + elements[0].dot(p_vec), + elements[1].dot(p_vec)); +} + +Vector2 Transform2D::xform(const Vector2 &p_vec) const { + + return Vector2( + tdotx(p_vec), + tdoty(p_vec)) + + elements[2]; +} +Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const { + + Vector2 v = p_vec - elements[2]; + + return Vector2( + elements[0].dot(v), + elements[1].dot(v)); +} +Rect2 Transform2D::xform(const Rect2 &p_rect) const { + + Vector2 x = elements[0] * p_rect.size.x; + Vector2 y = elements[1] * p_rect.size.y; + Vector2 pos = xform(p_rect.position); + + Rect2 new_rect; + new_rect.position = pos; + new_rect.expand_to(pos + x); + new_rect.expand_to(pos + y); + new_rect.expand_to(pos + x + y); + return new_rect; +} + +void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) { + + elements[0][0] = Math::cos(p_rot) * p_scale.x; + elements[1][1] = Math::cos(p_rot) * p_scale.y; + elements[1][0] = -Math::sin(p_rot) * p_scale.y; + elements[0][1] = Math::sin(p_rot) * p_scale.x; +} + +Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const { + + Vector2 ends[4] = { + xform_inv(p_rect.position), + xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)), + xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)), + xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)) + }; + + Rect2 new_rect; + new_rect.position = ends[0]; + new_rect.expand_to(ends[1]); + new_rect.expand_to(ends[2]); + new_rect.expand_to(ends[3]); + + return new_rect; +} + +#endif // TRANSFORM_2D_H |