add initial Shot class, fully untested

src/common/Shot.cc

@@ -0,0 +1,53 @@
+
+#include <math.h>
+#include "Shot.h"
+#include "Types.h"
+
+using namespace sf;
+
+/* INITIAL_SHOT_HEIGHT needs to be set to the height that the shot
+ * starts at, which will depend on the tank model in use */
+#define INITIAL_SHOT_HEIGHT 30
+
+#define GRAVITY 9.8
+
+/* We model the shot's position using a parametric equation based on time.
+ * Assuming a constant 45° shot angle simplifies the equations.
+ * x = Vt
+ * y = H + Vt - gt²/2
+ * where
+ * V = shot speed
+ * t = time
+ * g = gravity
+ * H = INITIAL_SHOT_HEIGHT
+ *
+ * According to the quadratic formula (x = (-b ± sqrt(b²-4ac))/2a), y = 0 when
+ * t = (-V + sqrt(V² - 4*g*H/2)) / (2*g/2)
+ * We need to solve for V.
+ * tg = sqrt(V² - 2gH) - V
+ * tg + V = sqrt(V² - 2gH)
+ * (tg + V)² = V² - 2gH
+ * t²g² + 2tgV + V² = V² - 2gH
+ * t²g² + 2tgV + 2gH = 0
+ * (t²g² + 2gH) = -2tgV
+ * -(t²g² + 2gH) / (2tg) = V
+ *
+ * So given the time to target (target_dist / PROJECTILE_VELOCITY) we can
+ * solve for what the shot's speed should be.
+ */
+Shot::Shot(const Vector2f & origin, double direction, double target_dist)
+{
+    m_direction = Vector2f(cos(direction), sin(direction));
+    m_origin = origin;
+    double t = target_dist / PROJECTILE_VELOCITY;
+    m_speed = -(t * t * GRAVITY * GRAVITY + 2 * GRAVITY * INITIAL_SHOT_HEIGHT)
+        / (2 * t * GRAVITY);
+}
+
+Vector3f Shot::get_pos_at_time(double time)
+{
+    float horiz_dist = m_speed * time;
+    float z = INITIAL_SHOT_HEIGHT + m_speed * time - GRAVITY * time * time / 2.0;
+    Vector2f xy = m_direction * horiz_dist;
+    return Vector3f(xy.x, xy.y, z);
+}

src/common/Shot.h

@@ -0,0 +1,18 @@
+
+#ifndef SHOT_H
+#define SHOT_H
+
+#include <SFML/System.hpp>
+
+class Shot
+{
+    public:
+        Shot(const sf::Vector2f & origin, double direction, double target_dist);
+        sf::Vector3f get_pos_at_time(double time);
+    protected:
+        sf::Vector2f m_origin;
+        sf::Vector2f m_direction;
+        double m_speed;
+};
+
+#endif