Adding idiomatic C++ equivalents for each subroutine in helpers.h.

docs/abi/example_elevate_nodes_curve.cpp

@@ -0,0 +1,34 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+#include "xtensor/xio.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 3> nodes {
+        { 0.0, 1.5, 3.0 },
+        { 0.0, 1.5, 0.0 },
+    };
+
+    // Outputs.
+    bezier::Matrix<2, 4> elevated = bezier::elevate_nodes_curve(nodes);
+
+    std::cout << "Elevated:" << std::endl;
+    std::cout << elevated << std::endl;
+
+    return 0;
+}

docs/abi/example_evaluate_curve_barycentric.cpp

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+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+#include "xtensor/xio.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 3> nodes {
+        { 0.0, 2.0, 3.0 },
+        { 1.0, 1.0, 3.0 },
+    };
+    bezier::Vector<4> lambda1 { 0.25, 0.5, 0.0, 1.0 };
+    bezier::Vector<4> lambda2 { 0.75, 0.25, 0.5, 0.25 };
+
+    // Outputs.
+    bezier::Matrix<2, 4> evaluated
+        = bezier::evaluate_curve_barycentric(nodes, lambda1, lambda2);
+
+    std::cout << "Evaluated:" << std::endl;
+    std::cout << evaluated << std::endl;
+
+    return 0;
+}

docs/abi/example_evaluate_hodograph.cpp

@@ -0,0 +1,35 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    double s = 0.125;
+    bezier::Matrix<2, 4> nodes {
+        { 1.0, 1.0, 2.0, 2.0 },
+        { 0.0, 1.0, 0.0, 1.0 },
+    };
+
+    // Outputs.
+    bezier::Vector<2> hodograph = bezier::evaluate_hodograph(s, nodes);
+
+    std::cout << "Hodograph:" << std::endl;
+    std::cout << hodograph[0] << std::endl;
+    std::cout << hodograph[1] << std::endl;
+
+    return 0;
+}

docs/abi/example_evaluate_multi.cpp

@@ -0,0 +1,35 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+#include "xtensor/xio.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 4> nodes {
+        { 1.0, 1.0, 2.0, 2.0 },
+        { 0.0, 1.0, 0.0, 1.0 },
+    };
+    bezier::Vector<3> s_vals { 0.0, 0.5, 1.0 };
+
+    // Outputs.
+    bezier::Matrix<2, 3> evaluated = bezier::evaluate_multi(nodes, s_vals);
+
+    std::cout << "Evaluated:" << std::endl;
+    std::cout << evaluated << std::endl;
+
+    return 0;
+}

docs/abi/example_full_reduce.cpp

@@ -0,0 +1,46 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+#include "xtensor/xio.hpp"
+#include "xtensor/xview.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 5> nodes {
+        { 1.0, 1.25, 1.5, 1.75, 2.0 },
+        { 3.0, 3.5, 4.0, 4.5, 5.0 },
+    };
+
+    // Outputs.
+    int num_reduced_nodes;
+    bezier::Matrix<2, 5> reduced;
+    bool not_implemented;
+
+    std::tuple<int, bool> status_pair = bezier::full_reduce(nodes, reduced);
+    num_reduced_nodes = std::get<0>(status_pair);
+    not_implemented = std::get<1>(status_pair);
+    auto reduced_view
+        = xt::view(reduced, xt::all(), xt::range(0, num_reduced_nodes));
+
+    std::cout << "Number of reduced nodes: " << num_reduced_nodes << std::endl;
+    std::cout << "Reduced:" << std::endl;
+    std::cout << reduced_view << std::endl;
+    std::cout << "Not implemented: " << (not_implemented ? "TRUE" : "FALSE")
+              << std::endl;
+
+    return 0;
+}

docs/abi/example_get_curvature.cpp

@@ -0,0 +1,34 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 5> nodes {
+        { 1.0, 0.75, 0.5, 0.25, 0.0 },
+        { 0.0, 2.0, -2.0, 2.0, 0.0 },
+    };
+    bezier::Vector<2> tangent_vec { -1.0, 0.0 };
+    double s = 0.5;
+
+    // Outputs.
+    double curvature = bezier::get_curvature(nodes, tangent_vec, s);
+
+    std::cout << "Curvature: " << curvature << std::endl;
+
+    return 0;
+}

docs/abi/example_locate_point_curve.cpp

@@ -0,0 +1,43 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 4> nodes {
+        { 0.0, -1.0, 1.0, -0.75 },
+        { 2.0, 0.0, 1.0, 1.625 },
+    };
+    bezier::Vector<2> point1 { -0.09375, 0.828125 };
+    bezier::Vector<2> point2 { 0.0, 1.5 };
+    bezier::Vector<2> point3 { -0.25, 1.375 };
+
+    // Outputs.
+    double s_approx;
+
+    s_approx = bezier::locate_point_curve(nodes, point1);
+    std::cout << "When B(s) = [" << point1[0] << ", " << point1[1]
+              << "]; s = " << s_approx << std::endl;
+    s_approx = bezier::locate_point_curve(nodes, point2);
+    std::cout << "When B(s) = [" << point2[0] << ", " << point2[1]
+              << "]; s = " << s_approx << std::endl;
+    s_approx = bezier::locate_point_curve(nodes, point3);
+    std::cout << "When B(s) = [" << point3[0] << ", " << point3[1]
+              << "]; s = " << s_approx << std::endl;
+
+    return 0;
+}

docs/abi/example_newton_refine_curve.cpp

@@ -0,0 +1,34 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 3> nodes {
+        { 0.0, 1.0, 3.0 },
+        { 0.0, 2.0, 1.0 },
+    };
+    bezier::Vector<2> point { 0.5625, 0.8125 };
+    double s = 0.75;
+
+    // Outputs.
+    double updated_s = bezier::newton_refine_curve(nodes, point, s);
+
+    std::cout << "Updated s: " << updated_s << std::endl;
+
+    return 0;
+}

docs/abi/example_reduce_pseudo_inverse.cpp

@@ -0,0 +1,39 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+#include "xtensor/xio.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 4> nodes {
+        { -3.0, 0.0, 1.0, 0.0 },
+        { 3.0, 2.0, 3.0, 6.0 },
+    };
+
+    // Outputs.
+    bezier::Matrix<2, 3> reduced;
+    bool not_implemented;
+
+    not_implemented = bezier::reduce_pseudo_inverse(nodes, reduced);
+
+    std::cout << "Reduced:" << std::endl;
+    std::cout << reduced << std::endl;
+    std::cout << "Not implemented: " << (not_implemented ? "TRUE" : "FALSE")
+              << std::endl;
+
+    return 0;
+}

docs/abi/example_specialize_curve.cpp

@@ -0,0 +1,37 @@
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+
+#include "bezier.hpp"
+#include "xtensor/xfixed.hpp"
+#include "xtensor/xio.hpp"
+
+int main(int argc, char* argv[])
+{
+    // Inputs.
+    bezier::Matrix<2, 3> nodes {
+        { 0.0, 0.5, 1.0 },
+        { 0.0, 1.0, 0.0 },
+    };
+    double start = -0.25;
+    double end = 0.75;
+
+    // Outputs.
+    bezier::Matrix<2, 3> new_nodes
+        = bezier::specialize_curve(nodes, start, end);
+
+    std::cout << "New Nodes:" << std::endl;
+    std::cout << new_nodes << std::endl;
+
+    return 0;
+}