1. Programming Proverbs
2. Collision prediction between circles
3. De-tour
4. Collision prediction between circles

Index

## 1. Programming Proverbs

• 17. ‘‘Never assume the computer assumes anything.''
• Henry F. Ledgard, ‘‘Programming Proverbs: Principles of Good Programming with Numerous Examples to Improve Programming Style and Proficiency'', (Hayden Computer Programming Series), Hayden Book Company, 1st edition, ISBN-13: 978-0810455221, December 1975.

## 2. Collision prediction between circles

• de-tour
• recall we can predict the time a point travels a distance by:
• • ```s = distance
u = initial velocity
a = acceleration
t = time```

## 3. De-tour

• if we were to drop a small ball bearing from 1 metre, how long would it take to hit the ground?
• initial velocity (u = 0)
• acceleration approx (a = 10) • thus
• • • • • • t = 0.45
• t = -0.45
• we also note that for more complicated quadratic equations we can use the formula:
• • for any equation matching: ## 4. Collision prediction between circles

• • each circle has a radius, position, velocity and acceleration
• radius is a scalar, all others are vectors
• remember that when these circles collide the distance between the two circle mid points will be • we know generally that the distance between the circles can be calculated as: • so we need to find the time when: • using the formula for initial position, velocity and acceleration: it is also known that the position circle at time, , is: • correspondingly the position circle at time, , is: • recall Pythagorean theorem can be used to find the length of the hypotenuse from the length of the base and height of a right angled triangle
• • • • is the radius of circle 0 and circle 1
• • is the difference of the y-axis position of the circles
• is the difference of the x-axis position of the circles
• therefore we need to find the time at which the distance between both circles is which is: