math/geometry: add support for 3-coordinate-space clipping
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@ -4,7 +4,7 @@
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namespace geometry {
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template <int L, typename T>
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template <typename T, int L>
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constexpr inline
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T line_plane_intersection_d(const vec<L, T>& plane_point, // p0
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const vec<L, T>& plane_normal, // n
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@ -19,7 +19,7 @@ T line_plane_intersection_d(const vec<L, T>& plane_point, // p0
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return intersection;
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}
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template <int L, typename T>
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template <typename T, int L>
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constexpr inline
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vec<L, T> line_plane_intersection(const vec<L, T>& plane_point, // p0
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const vec<L, T>& plane_normal, // n
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@ -34,32 +34,19 @@ vec<L, T> line_plane_intersection(const vec<L, T>& plane_point, // p0
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return line_start + line_vector * intersection;
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}
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template <int L, typename T, int M>
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template <typename T, int L>
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constexpr inline
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std::tuple<vec<L, T>, vec<M, T>> line_plane_intersection_two_lines(const vec<L, T>& plane_point, // p0
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const vec<L, T>& plane_normal, // n
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const vec<L, T>& line_start, // l0
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vec<L, T> interpolate(const vec<L, T>& line_start,
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const vec<L, T>& line_end,
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const vec<M, T>& line2_start,
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const vec<M, T>& line2_end
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T intersection
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)
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{
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/* it is assumed that line and line2 are the same line, but in different
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coordinates spaces. It is therefore possible to re-use the same
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interpolation value on either line vector.
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*/
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const auto line_vector = line_end - line_start; // l
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const auto line2_vector = line2_end - line2_start;
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const T intersection = line_plane_intersection_d(plane_point, plane_normal, line_start, line_vector); // d
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return { line_start + line_vector * intersection
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, line2_start + line2_vector * intersection
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};
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return line_start + line_vector * intersection;
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}
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template <int L, typename T>
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template <typename T, int L>
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T clip_boundary(const vec<L, T>& plane_point, // X
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const vec<L, T>& plane_normal, // Nc
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const vec<L, T>& line_point
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@ -74,7 +61,7 @@ inline T positive_modulo(T a, T b)
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return (a % b + b) % b;
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}
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template <int polygon_len, int L, typename T>
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template <int polygon_len, typename T, int L>
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inline int clip_polygon1(vec<L, T> * output,
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const vec<L, T> plane_point,
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const vec<L, T> plane_normal,
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@ -86,7 +73,7 @@ inline int clip_polygon1(vec<L, T> * output,
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const vec<L, T>& s = polygon[ix_s];
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const vec<L, T>& f = polygon[ix_f];
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bool this_inside = 0.f < clip_boundary<L, T>(plane_point,
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bool this_inside = 0.f < clip_boundary<T, L>(plane_point,
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plane_normal,
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f);
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@ -98,7 +85,7 @@ inline int clip_polygon1(vec<L, T> * output,
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case 0b01: // I, F
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length = 2;
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{
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const auto i = line_plane_intersection<L, T>(plane_point, plane_normal, s, f);
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const auto i = line_plane_intersection<T, L>(plane_point, plane_normal, s, f);
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*output++ = i;
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*output++ = f;
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}
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@ -106,7 +93,7 @@ inline int clip_polygon1(vec<L, T> * output,
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case 0b10: // I
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length = 1;
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{
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const auto i = line_plane_intersection<L, T>(plane_point, plane_normal, s, f);
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const auto i = line_plane_intersection<T, L>(plane_point, plane_normal, s, f);
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*output++ = i;
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}
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break;
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@ -119,7 +106,7 @@ inline int clip_polygon1(vec<L, T> * output,
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bool end_of_polygon = ix_f == (polygon_len - 1);
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if (!end_of_polygon) {
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return length +
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clip_polygon1<polygon_len, L, T>(output,
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clip_polygon1<polygon_len, T, L>(output,
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plane_point,
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plane_normal,
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polygon,
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@ -142,11 +129,11 @@ int clip_polygon(vec<L, T> * output,
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// It would be nice to remove the extra dot product, but the
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// alternative seems likely uglier.
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bool this_inside = 0.f < clip_boundary<L, T>(plane_point,
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bool this_inside = 0.f < clip_boundary<T, L>(plane_point,
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plane_normal,
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f);
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return clip_polygon1<polygon_len, L, T>(output,
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return clip_polygon1<polygon_len, T, L>(output,
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plane_point,
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plane_normal,
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polygon,
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@ -155,70 +142,70 @@ int clip_polygon(vec<L, T> * output,
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this_inside);
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}
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template <int polygon_len, int L, typename T, int M>
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inline int clip_polygon1_uv(vec<L, T> * output,
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vec<M, T> * output_uv,
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template <int polygon_len, typename T, int L, int M>
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inline int clip_polygon1_2(vec<L, T> * output_1,
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vec<M, T> * output_2,
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const vec<L, T> plane_point,
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const vec<L, T> plane_normal,
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const vec<L, T> * polygon,
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const vec<M, T> * polygon_uv,
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const vec<L, T> * polygon_1,
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const vec<M, T> * polygon_2,
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const int ix_s,
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const int ix_f,
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const bool last_inside)
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{
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const vec<L, T>& s = polygon[ix_s];
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const vec<L, T>& f = polygon[ix_f];
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const vec<L, T>& s_1 = polygon_1[ix_s];
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const vec<L, T>& f_1 = polygon_1[ix_f];
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const vec<M, T>& s_uv = polygon_uv[ix_s];
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const vec<M, T>& f_uv = polygon_uv[ix_f];
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const vec<M, T>& s_2 = polygon_2[ix_s];
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const vec<M, T>& f_2 = polygon_2[ix_f];
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bool this_inside = 0.f < clip_boundary<L, T>(plane_point,
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bool this_inside = 0.f < clip_boundary<T, L>(plane_point,
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plane_normal,
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f);
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f_1);
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int length = 0;
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switch ((last_inside << 1) | (this_inside << 0)) {
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int control = (last_inside << 1) | (this_inside << 0);
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switch (control) {
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case 0b00: // no output
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length = 0;
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break;
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case 0b01: // I, F
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length = 2;
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{
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auto [i, i_uv] = line_plane_intersection_two_lines<L, T, M>(plane_point, plane_normal,
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s, f,
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s_uv, f_uv);
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*output++ = i;
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*output_uv++ = i_uv;
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*output++ = f;
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*output_uv++ = f_uv;
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}
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break;
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case 0b10: // I
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length = 1;
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[[fallthrough]];
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case 0b01: // I, F
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{
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auto [i, i_uv] = line_plane_intersection_two_lines<L, T, M>(plane_point, plane_normal,
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s, f,
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s_uv, f_uv);
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*output++ = i;
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*output_uv++ = i_uv;
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const auto& i_1_start = s_1;
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const auto i_1_vector = f_1 - s_1; // l
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const T intersection = line_plane_intersection_d<T, L>(plane_point, plane_normal,
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i_1_start, i_1_vector);
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const vec<L, T> i_1 = i_1_start + i_1_vector * intersection;
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*output_1++ = i_1;
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*output_2++ = interpolate(s_2, f_2, intersection);
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if (control == 0b01) { // I, F
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*output_1++ = f_1;
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*output_2++ = f_2;
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length = 2;
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} else {
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length = 1;
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}
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}
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break;
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case 0b11: // F
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*output_1++ = f_1;
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*output_2++ = f_2;
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length = 1;
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*output++ = f;
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*output_uv++ = f_uv;
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break;
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}
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bool end_of_polygon = ix_f == (polygon_len - 1);
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if (!end_of_polygon) {
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return length +
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clip_polygon1_uv<polygon_len, L, T, M>(output,
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output_uv,
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clip_polygon1_2<polygon_len, T, L, M>(output_1,
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output_2,
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plane_point,
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plane_normal,
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polygon,
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polygon_uv,
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polygon_1,
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polygon_2,
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ix_f,
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ix_f + 1,
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this_inside);
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@ -227,29 +214,144 @@ inline int clip_polygon1_uv(vec<L, T> * output,
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}
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}
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template <int polygon_len, int L, typename T, int M>
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int clip_polygon_uv(vec<L, T> * output,
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vec<M, T> * output_uv,
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template <int polygon_len, typename T, int L, int M>
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int clip_polygon_2(vec<L, T> * output_1,
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vec<M, T> * output_2,
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const vec<L, T>& plane_point,
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const vec<L, T>& plane_normal,
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const vec<L, T> * polygon,
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const vec<M, T> * polygon_uv
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const vec<L, T> * polygon_1,
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const vec<M, T> * polygon_2
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)
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{
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const vec<L, T> f = polygon[polygon_len - 1];
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const vec<L, T> f = polygon_1[polygon_len - 1];
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// It would be nice to remove the extra dot product, but the
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// alternative seems likely uglier.
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bool this_inside = 0.f < clip_boundary<L, T>(plane_point,
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bool this_inside = 0.f < clip_boundary<T, L>(plane_point,
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plane_normal,
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f);
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return clip_polygon1_uv<polygon_len, L, T, M>(output,
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output_uv,
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return clip_polygon1_2<polygon_len, T, L, M>(output_1,
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output_2,
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plane_point,
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plane_normal,
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polygon,
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polygon_uv,
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polygon_1,
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polygon_2,
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polygon_len - 1, // ix_s
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0, // ix_f
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this_inside);
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}
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template <int polygon_len, typename T, int L, int M, int N>
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inline int clip_polygon1_3(vec<L, T> * output_1,
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vec<M, T> * output_2,
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vec<N, T> * output_3,
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const vec<L, T> plane_point,
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const vec<L, T> plane_normal,
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const vec<L, T> * polygon_1,
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const vec<M, T> * polygon_2,
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const vec<N, T> * polygon_3,
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const int ix_s,
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const int ix_f,
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const bool last_inside)
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{
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const vec<L, T>& s_1 = polygon_1[ix_s];
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const vec<L, T>& f_1 = polygon_1[ix_f];
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const vec<M, T>& s_2 = polygon_2[ix_s];
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const vec<M, T>& f_2 = polygon_2[ix_f];
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const vec<N, T>& s_3 = polygon_3[ix_s];
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const vec<N, T>& f_3 = polygon_3[ix_f];
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bool this_inside = 0.f < clip_boundary<T, L>(plane_point,
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plane_normal,
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f_1);
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int length = 0;
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int control = (last_inside << 1) | (this_inside << 0);
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switch (control) {
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case 0b00: // no output
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length = 0;
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break;
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case 0b10: // I
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[[fallthrough]];
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case 0b01: // I, F
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{
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const auto& i_1_start = s_1;
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const auto i_1_vector = f_1 - s_1; // l
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const T intersection = line_plane_intersection_d<T, L>(plane_point, plane_normal,
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i_1_start, i_1_vector);
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const vec<L, T> i_1 = i_1_start + i_1_vector * intersection;
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*output_1++ = i_1;
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*output_2++ = interpolate(s_2, f_2, intersection);
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*output_3++ = interpolate(s_3, f_3, intersection);
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if (control == 0b01) { // I, F
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*output_1++ = f_1;
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*output_2++ = f_2;
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*output_3++ = f_3;
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length = 2;
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} else {
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length = 1;
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}
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}
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break;
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case 0b11: // F
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*output_1++ = f_1;
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*output_2++ = f_2;
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*output_3++ = f_3;
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length = 1;
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break;
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}
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bool end_of_polygon = ix_f == (polygon_len - 1);
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if (!end_of_polygon) {
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return length +
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clip_polygon1_3<polygon_len, T, L, M, N>(output_1,
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output_2,
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output_3,
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plane_point,
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plane_normal,
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polygon_1,
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polygon_2,
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polygon_3,
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ix_f,
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ix_f + 1,
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this_inside);
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} else {
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return length;
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}
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}
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template <int polygon_len, typename T, int L, int M, int N>
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int clip_polygon_3(vec<L, T> * output_1,
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vec<M, T> * output_2,
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vec<N, T> * output_3,
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const vec<L, T>& plane_point,
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const vec<L, T>& plane_normal,
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const vec<L, T> * polygon_1,
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const vec<M, T> * polygon_2,
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const vec<N, T> * polygon_3
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)
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{
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const vec<L, T> f = polygon_1[polygon_len - 1];
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// It would be nice to remove the extra dot product, but the
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// alternative seems likely uglier.
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bool this_inside = 0.f < clip_boundary<T, L>(plane_point,
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plane_normal,
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f);
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return clip_polygon1_3<polygon_len, T, L, M>(output_1,
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output_2,
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output_3,
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plane_point,
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plane_normal,
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polygon_1,
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polygon_2,
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polygon_3,
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polygon_len - 1, // ix_s
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0, // ix_f
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this_inside);
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