Split 2022 vision math code into library

This allows it to be used in target estimator and camera reader in a
addition to blob detector. Will be used for comparing size of projected
blobs to detected blobs, as well as for interpolating between localizer
outputs.

Signed-off-by: milind-u <milind.upadhyay@gmail.com>
Change-Id: I80a726e93d638106431614459837e8671bcb7251
diff --git a/y2022/vision/geometry.h b/y2022/vision/geometry.h
new file mode 100644
index 0000000..75a6496
--- /dev/null
+++ b/y2022/vision/geometry.h
@@ -0,0 +1,129 @@
+#include "aos/util/math.h"
+#include "glog/logging.h"
+#include "opencv2/core/types.hpp"
+
+namespace y2022::vision {
+
+// Linear equation in the form y = mx + b
+struct SlopeInterceptLine {
+  double m, b;
+
+  inline SlopeInterceptLine(cv::Point2d p, cv::Point2d q) {
+    if (p.x == q.x) {
+      CHECK_EQ(p.y, q.y) << "Can't fit line to infinite slope";
+
+      // If two identical points were passed in, give the slope 0,
+      // with it passing the point.
+      m = 0.0;
+    } else {
+      m = (p.y - q.y) / (p.x - q.x);
+    }
+    // y = mx + b -> b = y - mx
+    b = p.y - (m * p.x);
+  }
+
+  inline double operator()(double x) const { return (m * x) + b; }
+};
+
+// Linear equation in the form ax + by = c
+struct StdFormLine {
+ public:
+  double a, b, c;
+
+  inline std::optional<cv::Point2d> Intersection(const StdFormLine &l) const {
+    // Use Cramer's rule to solve for the intersection
+    const double denominator = Determinant(a, b, l.a, l.b);
+    const double numerator_x = Determinant(c, b, l.c, l.b);
+    const double numerator_y = Determinant(a, c, l.a, l.c);
+
+    std::optional<cv::Point2d> intersection = std::nullopt;
+    // Return nullopt if the denominator is 0, meaning the same slopes
+    if (denominator != 0) {
+      intersection =
+          cv::Point2d(numerator_x / denominator, numerator_y / denominator);
+    }
+
+    return intersection;
+  }
+
+ private:  // Determinant of [[a, b], [c, d]]
+  static inline double Determinant(double a, double b, double c, double d) {
+    return (a * d) - (b * c);
+  }
+};
+
+struct Circle {
+ public:
+  cv::Point2d center;
+  double radius;
+
+  static inline std::optional<Circle> Fit(std::vector<cv::Point2d> points) {
+    CHECK_EQ(points.size(), 3ul);
+    // For the 3 points, we have 3 equations in the form
+    // (x - h)^2 + (y - k)^2 = r^2
+    // Manipulate them to solve for the center and radius
+    // (x1 - h)^2 + (y1 - k)^2 = r^2 ->
+    // x1^2 + h^2 - 2x1h + y1^2 + k^2 - 2y1k = r^2
+    // Also, (x2 - h)^2 + (y2 - k)^2 = r^2
+    // Subtracting these two, we get
+    // x1^2 - x2^2 - 2h(x1 - x2) + y1^2 - y2^2 - 2k(y1 - y2) = 0 ->
+    // h(x1 - x2) + k(y1 - y2) = (-x1^2 + x2^2 - y1^2 + y2^2) / -2
+    // Doing the same with equations 1 and 3, we get the second linear equation
+    // h(x1 - x3) + k(y1 - y3) = (-x1^2 + x3^2 - y1^2 + y3^2) / -2
+    // Now, we can solve for their intersection and find the center
+    const auto l =
+        StdFormLine{points[0].x - points[1].x, points[0].y - points[1].y,
+                    (-std::pow(points[0].x, 2) + std::pow(points[1].x, 2) -
+                     std::pow(points[0].y, 2) + std::pow(points[1].y, 2)) /
+                        -2.0};
+    const auto m =
+        StdFormLine{points[0].x - points[2].x, points[0].y - points[2].y,
+                    (-std::pow(points[0].x, 2) + std::pow(points[2].x, 2) -
+                     std::pow(points[0].y, 2) + std::pow(points[2].y, 2)) /
+                        -2.0};
+    const auto center = l.Intersection(m);
+
+    std::optional<Circle> circle = std::nullopt;
+    if (center) {
+      // Now find the radius
+      const double radius = cv::norm(points[0] - *center);
+      circle = Circle{*center, radius};
+    }
+    return circle;
+  }
+
+  inline double DistanceTo(cv::Point2d p) const {
+    const auto p_prime = TranslateToOrigin(p);
+    // Now, the distance is simply the difference between distance from the
+    // origin to p' and the radius.
+    return std::abs(cv::norm(p_prime) - radius);
+  }
+
+  inline double AngleOf(cv::Point2d p) const {
+    auto p_prime = TranslateToOrigin(p);
+    // Flip the y because y values go downwards.
+    p_prime.y *= -1;
+    return std::atan2(p_prime.y, p_prime.x);
+  }
+
+  inline bool InAngleRange(cv::Point2d p, double theta_min,
+                           double theta_max) const {
+    const double theta = AngleOf(p);
+
+    // Handle the case if the bounds wrap around 2pi
+    const double max_diff = aos::math::NormalizeAngle(theta_max - theta);
+    const double min_diff = aos::math::NormalizeAngle(theta - theta_min);
+
+    return ((theta == theta_max) || (theta == theta_min) ||
+            (std::signbit(min_diff) == std::signbit(max_diff)));
+  }
+
+ private:
+  // Translate the point on the circle
+  // as if the circle's center is the origin (0,0)
+  inline cv::Point2d TranslateToOrigin(cv::Point2d p) const {
+    return cv::Point2d(p.x - center.x, p.y - center.y);
+  }
+};
+
+}  // namespace y2022::vision