Trigonometry and Applications References: xyz. Review (?) from ETGG1801 Angles – As a measure of rotation and/or orientation – Radians & Degrees (and.

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Trigonometry and Applications References: xyz

Review (?) from ETGG1801 Angles – As a measure of rotation and/or orientation – Radians & Degrees (and conversions) Trig functions – sin, cos, tan, sin -1, cos -1,tan -1 Polar and Cartesian coordinates – Points in a cartesian system – Conversions between them – atan2 (python) function – Pythagorean theorem

Trig Application#1 : Vector Motion Cardinal-direction movement: "Free" movement:

Vector motion

Variable frame rates (review) Two options for handling it: – Option1: Cap frame rates When moving / rotating express in units / updated Good: Easy to understand Bad: Slow machines can't reach the frame-rate – Option2: Let computer run as fast as possible When moving / rotating express in units / second – The multiply by the time since the last frame Good: Runs on any speed machine Bad: A little harder to understand This is the one I'm going to make you use

Velocity and Acceleration Suppose you are moving at 50mph for 3 hours. How far are you from your original position? – A: 150 miles 50 * 3 Express this as a graph – We're really calculating the area of this rectangle. Speed (mph) Time (hours) 50 3

Velocity and Acceleration, cont. What about (abruptly) changing velocity? Speed (mph) Time (hours) 50 3 Q: How far have we travelled after these 5 hours? Q (rephrased): In other words, what is the area of the pink area? A: 0.5*(50x1) + (50x3) + 0.5*(50x1) = 200 miles

Velocity and Acceleration, cont. we can approximate the area of this curve using (small) discreet time intervals Speed (mph) Time (hours) 50 3

Velocity and Acceleration, cont.

Speed (mph) Time (hours) 50 3 Position-offset (miles) Time (hours)

Velocity and Acceleration

Velocity and Acceleration, cont. Acceleration is a change in velocity Speed (mph) Time (hours) 50 3 Position-offset (miles) Time (hours) Accel (m/h 2 ) 3 50

Acceleration and Vectors, cont.

Trig Application#2 : Orienting object A such that it points towards object

Trig Application#3: Rotate-able object

Newton's Laws of Motion

New Lab 1.Physics "mix-in" class – pos, velocity, mass 2.Bounding volume "mix-in" class – 2d circle Main program: – Create a bunch of circles, subject to gravity and bouncing off walls – Click to lay a bomb.