From 1741476456954a2cbb2a8099e7cef535e84fd818 Mon Sep 17 00:00:00 2001
From: Josh Holtrop <jholtrop@gmail.com>
Date: Sat, 6 Oct 2012 22:47:29 -0400
Subject: [PATCH] trying to fix Shot position calculation, better, but still
 wrong

---
 src/common/Shot.cc | 28 ++++++++++++++++------------
 1 file changed, 16 insertions(+), 12 deletions(-)

diff --git a/src/common/Shot.cc b/src/common/Shot.cc
index 763bde4..c68996e 100644
--- a/src/common/Shot.cc
+++ b/src/common/Shot.cc
@@ -7,7 +7,7 @@ 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 INITIAL_SHOT_HEIGHT 10
 
 #define GRAVITY 9.8
 
@@ -15,22 +15,26 @@ using namespace sf;
  * Assuming a constant 45° shot angle simplifies the equations.
  * x = Vt
  * y = H + Vt - gt²/2
+ *   = (-g/2)t² + Vt + H
  * where
  * V = shot speed
  * t = time
  * g = gravity
  * H = INITIAL_SHOT_HEIGHT
  *
+ * We want to figure out a speed that gets us to y = 0 at our desired time.
  * 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
+ * t = (-V ± sqrt(V² - 4(-g/2)H)) / 2(-g/2)
+ * -tg = -V ± sqrt(V² + 2gH)
+ * V - tg = ± sqrt(V² + 2gH)
+ *
+ * V - tg = sqrt(V² + 2gH)
+ * (V - tg)² = V² + 2gH
+ * V² - 2Vtg + t²g² = V² + 2gH
+ * t²g² - 2Vtg = 2gH
+ * -2Vtg = 2gH - t²g²
+ * V = -(2gH - t²g²)/2tg
+ * V = (t²g² - 2gH)/2tg
  *
  * So given the time to target (target_dist / PROJECTILE_VELOCITY) we can
  * solve for what the shot's speed should be.
@@ -40,7 +44,7 @@ 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)
+    m_speed = (t * t * GRAVITY * GRAVITY - 2 * GRAVITY * INITIAL_SHOT_HEIGHT)
         / (2 * t * GRAVITY);
 }
 
@@ -49,6 +53,6 @@ Vector3f Shot::get_position()
     float time = m_clock.getElapsedTime().asSeconds();
     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;
+    Vector2f xy = m_origin + m_direction * horiz_dist;
     return Vector3f(xy.x, xy.y, z);
 }