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Quiz: Polar Coordinates, Oscillation & Easing

Test your understanding of Polar geometry, spirals, easing algorithms, lerp(), and smooth interpolation with these review questions.

1. What does the lerp(start, stop, amt) function compute?

  1. Linear interpolation between two values based on a percentage amount (0.0 to 1.0)
  2. The trigonometric tangent of an angle
  3. The Euclidean distance between two points
  4. The maximum of two integers
Show Answer

The correct answer is A. lerp(a, b, amt) calculates a number between a and b at normalized progression amt (where 0.0 is a and 1.0 is b). Options A, C, and D describe other mathematical operations.

Concept Tested: Linear Interpolation Lerp

2. Which function calculates the straight-line Euclidean distance between two points (x1, y1) and (x2, y2) in p5.js?

  1. dist(x1, y1, x2, y2)
  2. mag()
  3. diff(x1, y1, x2, y2)
  4. length()
Show Answer

The correct answer is A. dist(x1, y1, x2, y2) uses the Pythagorean theorem sqrt((x2-x1)^2 + (y2-y1)^2) to calculate Euclidean distance between two 2D coordinates. Options A, C, and D are incorrect function signatures.

Concept Tested: Distance Formula Dist

3. What type of curve is generated when radius r increases proportionally as angle theta increases in polar coordinates (r = a * theta)?

  1. Parabola
  2. Archimedean spiral
  3. Sine wave
  4. Hyperbola
Show Answer

The correct answer is B. An Archimedean spiral is formed when the radius grows linearly as the angle sweeps around the origin. Options B, C, and D are non-spiral geometric forms.

Concept Tested: Archimedean Spiral

4. To create smooth 'easing' where a circle lags behind and glides toward mouseX, which code snippet is placed in draw()?

  1. x = mouseX;
  2. x += (mouseX - x) * 0.05;
  3. x = lerp(x, 0, 0.05);
  4. x += mouseX * 0.05;
Show Answer

The correct answer is B. Adding a fraction of the distance between current position and target (x += (target - x) * easing) creates an exponential ease-out curve where motion is fast initially and decelerates smoothly as it nears the target. Options B, C, and D do not create smooth target tracking.

Concept Tested: Easing Interpolation

5. Which p5.js function restricts a numeric value to remain between a minimum and maximum boundary?

  1. clamp(val, min, max)
  2. constrain(val, min, max)
  3. limit(val, min, max)
  4. bound(val, min, max)
Show Answer

The correct answer is B. constrain(val, min, max) clamps a value so that if it is lower than min it returns min, and if higher than max it returns max. Options B, C, and D are not built-in p5.js functions.

Concept Tested: Constrain Value Function

6. Why is checking squared distance (dx*dx + dy*dy < r*r) preferred in high-performance particle collision loops over calling dist()?

  1. dist() only works in 3D WebGL mode
  2. Squared distance automatically sorts the particles
  3. It avoids the computationally expensive square root calculation (Math.sqrt)
  4. dist() allocates extra heap memory on every call
Show Answer

The correct answer is C. Calculating dist() requires sqrt(), which is relatively expensive when repeated across thousands of particle pairs per frame. Comparing dx*dx + dy*dy against (r1+r2)*(r1+r2) gives the identical collision boolean result without calculating square roots. Options B, C, and D are incorrect.

Concept Tested: Square Distance Metric

7. What value does norm(value, low, high) return if value = 150, low = 100, and high = 200?

  1. 50
  2. 1.5
  3. 0.5
  4. 0.25
Show Answer

The correct answer is C. norm(val, low, high) maps a value in [low, high] to the normalized range [0.0, 1.0]. Since 150 is halfway between 100 and 200, norm returns 0.5. Options B, C, and D are incorrect calculations.

Concept Tested: Normalize Function Norm

8. What does the map(value, start1, stop1, start2, stop2) function do?

  1. It downloads a geographic map from Google Maps
  2. It iterates through an array like Array.prototype.map
  3. It re-maps a number from an incoming source range to a target destination range
  4. It renders an image texture onto a 3D plane
Show Answer

The correct answer is C. map() linearly scales a value from one domain [start1, stop1] to a new range [start2, stop2]. For example, map(mouseX, 0, width, 0, 255) maps screen position to RGB color range. Options A, C, and D confuse this with other mapping concepts.

Concept Tested: Map Function

9. In a polar coordinate system, what happens to the rendered point if the radius r is set to a constant value while angle theta sweeps from 0 to TWO_PI?

  1. It draws a square boundary
  2. It draws an outward straight line
  3. It draws a parabola
  4. It draws a perfect circle around the origin
Show Answer

The correct answer is D. Keeping radius constant while angle sweeps from 0 to 2*PI traces a circle of radius r centered at the origin. Options B, C, and D are incorrect.

Concept Tested: Polar Circle Geometry

10. A developer applies x = lerp(x, targetX, 0.1); on each frame. If targetX = 100 and x starts at 0, what is the value of x after the first frame?

  1. 100
  2. 1
  3. 90
  4. 10
Show Answer

The correct answer is D. lerp(0, 100, 0.1) computes 0 + (100 - 0) * 0.1 = 10. On the second frame x would become 10 + (100 - 10) * 0.1 = 19. Options B, C, and D are incorrect.

Concept Tested: Lerp Calculation Step