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Aiming Cannons at Worms (with Wind) - Projectile Motion in Games

• 0:00:04 Introduction: This video builds upon a previous one, addressing how to calculate a cannon's firing angle to hit a target, now considering wind.

• 0:00:37 Previous Solution: The previous video's solution (calculateTrajectory function) worked when only gravity (a vertical force) was present. It used a quadratic equation to solve for two possible firing angles.

• 0:03:53 Problem with Wind: Wind introduces a horizontal force, making the previous, simple, x-axis solution invalid (speed = distance / time no longer applies, and instead s = ut + 1/2at^2 must be used). This means solving another, more complicated quadratic equation.

• 0:05:25 A Different Approach: Instead of re-deriving complex equations, the video proposes a visual and more intuitive solution: frame transformation (rotation).

• 0:06:51 Core Idea: Rotation: The core concept is to rotate the entire scene (including the target) so that the combined force vector (gravity + wind) points straight down, aligning with the original gravity-only scenario.

• 0:07:36 Scene Rotation: The scene is rotated by an angle (theta) calculated based on the combined force vector. This effectively makes the problem a "gravity-only" problem in a new, rotated frame of reference.

• 0:07:59 Using Existing Code: The original calculateTrajectory function can still be used in this rotated frame, because it only deals with a downward force.

• 0:08:17 Rotating Back: The calculated firing angles (from the rotated frame) are then rotated back by the original rotation angle (theta) to get the correct angles in the original, unrotated frame.

• 0:08:41 "Delta Light 2" Showcase: Briefly showcases "Delta Light 2," a bullet hell game by Discord members, built using the Luminovu engine (similar to Pixel Game Engine).

• 0:11:56 Code Implementation: The video demonstrates the code changes, starting with the previous video's code.

• 0:12:04 Adding Wind: A wind component is added to the force vector used in the projectile's trajectory calculation.

• 0:13:09 Modifying calculateTrajectory:

  • The function now accepts a 2D force vector, not just a gravity scalar.
  • force_angle is calculated using atan2(force.y, force.x).
  • The target is rotated using cartesian and polar coordinate conversions.
  • The resulting angles are rotated back by force_angle.

• 0:15:58 A 90 degree problem The AAN 2 function may return angles 90° from expectations.

• 0:16:27 Visualizing the Force Vector: Code is added to draw a cyan line representing the combined force vector (midpoint between source and target).

• 0:16:58 Adding Wind Controls: Arrow keys and spacebar are used to control the wind's strength and direction.

• 0:17:10 Demonstration: The final application shows how the firing angles are correctly calculated, even with varying wind conditions.

• 0:18:10 Assumptions The model assumes that their is no wind resistance and wind doesn't change during the trajectory of the projectile.

• 0:18:24 Conclusion: The solution is surprisingly simple and effective, requiring minimal code changes. Source code and a PGE Tinker version will be provided.