bezier: add intersection count test
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104
bezier.cpp
104
bezier.cpp
@ -138,6 +138,110 @@ namespace util {
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}
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//-----------------------------------------------------------------------------
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namespace util {
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template <>
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std::array<util::vector2f,4>
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bezier<3>::coeffs (void) const
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{
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auto &v = reinterpret_cast<const util::vector2f(&)[4]> (m_points);
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return {
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-1 * v[0] +3 * v[1] -3 * v[2] +1 * v[3],
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3 * v[0] -6 * v[1] +3 * v[2],
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-3 * v[0] +3 * v[1],
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1 * v[0]
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};
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}
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}
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//-----------------------------------------------------------------------------
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namespace util {
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template <>
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std::array<util::vector2f,3>
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bezier<2>::coeffs (void) const
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{
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auto &v = reinterpret_cast<const util::vector2f(&)[3]> (m_points);
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return {
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+1 * v[2] -2 * v[1] + 1 * v[0],
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-2 * v[2] +2 * v[1],
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+1 * v[2]
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};
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}
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}
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//-----------------------------------------------------------------------------
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namespace util {
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template <>
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std::array<util::vector2f,2>
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bezier<1>::coeffs (void) const
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{
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auto &v = reinterpret_cast<const util::vector2f(&)[2]> (m_points);
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return {
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-1 * v[1] + 1 * v[0],
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+1 * v[1],
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};
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}
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}
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//-----------------------------------------------------------------------------
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// XXX: If the line is co-linear we'll have no solutions. But we return 1
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// anyway as this function is used to find any point that intersects as part
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// of other more comprehensive tests.
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template <size_t S>
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size_t
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util::bezier<S>::intersections (point2f p0, point2f p1) const
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{
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float A = p1.y - p0.y; // A = y2 - y1
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float B = p0.x - p1.x; // B = x1 - x2
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float C = p0.x * (p0.y - p1.y) + // C = x1 (y1 - y2) + y1 (x2 - x1)
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p0.y * (p1.x - p0.x);
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// Build the intersection polynomial
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const std::array<vector2f,S+1> bcoeff = coeffs ();
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std::array<float,S+1> pcoeff;
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for (size_t i = 0; i < pcoeff.size (); ++i)
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pcoeff[i] = A * bcoeff[i].x + B * bcoeff[i].y;
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pcoeff.back () += C;
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const auto r = polynomial::solve<S> (pcoeff);
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// The curve and line are colinear
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if (std::all_of (r.begin (), r.end (), [] (auto i) { return std::isnan (i); }))
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return 1;
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size_t count = 0;
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for (size_t i = 0; i < S; ++i) {
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// Ensure the solutions are on the curve
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const auto t = r[i];
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if (std::isnan (t))
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break;
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if (t < 0.f || t > 1.f)
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continue;
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// Find the line's intersection point
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const util::vector2f q = polynomial::eval (bcoeff, t);
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const auto s = almost_equal (p0.x, p1.x) ?
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(q.y-p0.y) / (p1.y-p0.y) :
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(q.x-p0.x) / (p1.x-p0.x) ; // vertical
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// Check if the point is on the line
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if (s >= 0.f && s <= 1.f)
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++count;
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}
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return count;
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}
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//-----------------------------------------------------------------------------
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namespace util {
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// TODO: use a more reliable method like [Xiao-Dia Chen 2010]
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@ -31,6 +31,13 @@ namespace util {
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bezier (const util::point2f (&)[S+1]);
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point2f eval (float t) const;
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// Calculate the expanded polynomial coeffecients in terms of t
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std::array<vector2f,S+1>
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coeffs (void) const;
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size_t intersections (point2f from, point2f to) const;
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float distance (point2f) const;
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point2f& operator[] (size_t idx);
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127
test/bezier.cpp
127
test/bezier.cpp
@ -4,10 +4,16 @@
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#include <cstdlib>
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int
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main (int, char**)
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{
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// Check degree-1 beziers
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//-----------------------------------------------------------------------------
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template <size_t> void test_eval (void);
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template <size_t> void test_intersect (void);
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//-----------------------------------------------------------------------------
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template <>
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void
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test_eval<1> (void)
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{
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static const util::bezier<1> b1 ({{ 0.f, 0.f},
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{100.f, 100.f}});
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@ -23,7 +29,11 @@ main (int, char**)
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CHECK_EQ (px, rx);
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}
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// Check degree-2 beziers
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//-----------------------------------------------------------------------------
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template <>
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void
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test_eval<2> (void)
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{
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static const util::bezier<2> b2 ({{ 0.f, 0.f},
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{ 50.f, 50.f},
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@ -40,7 +50,11 @@ main (int, char**)
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CHECK_EQ (px, rx);
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}
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// Check degree-3 beziers
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//-----------------------------------------------------------------------------
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template <>
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void
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test_eval<3> (void)
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{
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static const util::bezier<3> b3 ({{ 0.f, 0.f },
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{ 33.f, 33.f },
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@ -58,5 +72,106 @@ main (int, char**)
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CHECK_EQ (px, rx);
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}
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//-----------------------------------------------------------------------------
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template <>
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void
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test_intersect<1> (void)
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{
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// A line from (0,0) to (100,100)
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static const util::bezier<1> b1 ({{0.f, 0.f}, {100.f, 100.f}});
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// Through the centre
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CHECK_EQ (b1.intersections ({0.f, 100.f}, {100.f, 0.f}), 1);
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CHECK_EQ (b1.intersections ({100.f, 0.f}, {0.f, 100.f}), 1);
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// Coincident with endpoints
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CHECK_EQ (b1.intersections ({0.f, 0.f}, {1.f,0.f}), 1);
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CHECK_EQ (b1.intersections ({100.f, 100.f}, {100.f,0.f}), 1);
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// Co-planar
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CHECK_EQ (b1.intersections ({0.f, 0.f}, {1.f, 1.f}), 1);
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// Underneath
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CHECK_EQ (b1.intersections ({1000.f, -10.f}, {-1000.f, -10.f}), 0);
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// Above
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CHECK_EQ (b1.intersections ({1000.f, 110.f}, {-1000.f, 110.f}), 0);
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}
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//-----------------------------------------------------------------------------
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template <>
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void
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test_intersect<2> (void)
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{
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// A linear curve from (0,0) to (100,100)
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static const util::bezier<2> b2 ({{ 0.0f, 0.0f},
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{ 50.f, 50.f},
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{100.f, 100.f}});
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// Through the centre
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CHECK_EQ (b2.intersections ({100.f, 0.f}, {0.f, 100.f}), 1);
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CHECK_EQ (b2.intersections ({0.f, 100.f}, {100.f, 0.f}), 1);
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// Coincident with endpoints
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CHECK_EQ (b2.intersections ({0.f, 0.f}, {0.f,100.f}), 1);
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CHECK_EQ (b2.intersections ({0.f, 0.f}, {100.f,0.f}), 1);
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CHECK_EQ (b2.intersections ({100.f, 100.f}, {100.f,0.f}), 1);
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// Co-planar
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CHECK_EQ (b2.intersections ({0.f, 0.f}, {1.f, 1.f}), 1);
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// Underneath
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CHECK_EQ (b2.intersections ({1000.f, -10.f}, {-1000.f, -10.f}), 0);
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// Above
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CHECK_EQ (b2.intersections ({1000.f, 110.f}, {-1000.f, 110.f}), 0);
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}
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//-----------------------------------------------------------------------------
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template <>
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void
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test_intersect<3> (void)
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{
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// A linear curve from (0,0) to (100,100)
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static const util::bezier<3> b3 ({{ 0.f, 0.f },
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{ 33.f, 33.f },
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{ 67.f, 67.f },
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{ 100.f, 100.f }});
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// Through the centre
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CHECK_EQ (b3.intersections ({100.f, 0.f}, {0.f, 100.f}), 1);
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CHECK_EQ (b3.intersections ({0.f, 100.f}, {100.f, 0.f}), 1);
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// Coincident with endpoints
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CHECK_EQ (b3.intersections ({0.f, 0.f}, {0.f,100.f}), 1);
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CHECK_EQ (b3.intersections ({0.f, 0.f}, {100.f,0.f}), 1);
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CHECK_EQ (b3.intersections ({100.f, 100.f}, {100.f,0.f}), 1);
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// Co-planar
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CHECK_EQ (b3.intersections ({0.f, 0.f}, {1.f, 1.f}), 1);
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// Underneath
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CHECK_EQ (b3.intersections ({1000.f, -10.f}, {-1000.f, -10.f}), 0);
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// Above
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CHECK_EQ (b3.intersections ({1000.f, 110.f}, {-1000.f, 110.f}), 0);
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}
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//-----------------------------------------------------------------------------
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int
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main (int, char**)
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{
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test_eval<1> ();
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test_eval<2> ();
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test_eval<3> ();
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test_intersect<1> ();
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test_intersect<2> ();
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test_intersect<3> ();
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return EXIT_SUCCESS;
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}
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