Name what you already understand before the build gets bigger.
Maker math
Motion Tracking with Vector Velocity
Turn two position samples into direction, speed, and a useful motion note for games, robots, camera tracking, or sensor logs.
Topic goal to ladder route
Know the destination, then climb the route.
A topic is the maker goal. A ladder is the route from what you understand now to one visible proof you can build, sketch, test, or explain. This one ties back to Build a First Godot Game Loop.
Compare two positions, compute the delta vector, divide by elapsed time, and explain speed and direction without hiding units or uncertainty.
Read the short lesson, watch one useful source, sketch the idea, check the math, then practice.
Enter a current point, target point, and speed in the graph widget. Then write the delta vector, length, unit direction, next position, and what extra samples you would need before trusting the motion.
Text lesson first
What this math unlocks
Turn two position samples into direction, speed, and a useful motion note for games, robots, camera tracking, or sensor logs. The useful question is not “what formula do I memorize?” It is “what part of the build can I now inspect, predict, or measure?”
Project question
Compare two positions, compute the delta vector, divide by elapsed time, and explain speed and direction without hiding units or uncertainty.
Safe first move
Write the two positions, units, and elapsed time before calculating speed or smoothing the track.
Use it in context
Build a First Godot Game Loop gives this idea a concrete project anchor.
Source tutorials for this topic
These videos support the lesson. Use them to see the idea move, then keep the written ladder, notes, cards, and practice task as the reusable part.
Use the controls to compare source tutorials. The first card embeds a privacy-enhanced player; alternate cards open on YouTube so the page stays fast.
1 of 3
Primary source
Math for Game Devs Part 1: Numbers, Vectors and Dot Product
Video by Freya Holmer · Open on YouTube
A visual bridge from coordinates to vectors and dot products, useful for movement, facing checks, lighting, sensor direction, and force arrows.
First watch: Watch for the moment a vector becomes both direction and length, then write what a normalized vector proves.
- Vector length and direction
- Normalization
- Dot product meaning
- Practical facing or projection use
Practice after watching: Draw two arrows from a project and write what their length, direction, and dot product answer.
Preference saves on this device.
Open on YouTube
Alternate source
Vectors, what even are they?
Video by 3Blue1Brown · Open on YouTube
Good for learners who need the visual meaning of a vector before using one in a game, sensor, CAD, or motion problem.
First watch: Watch for the difference between an arrow, a list of numbers, and a movement instruction.
- Vector as arrow
- Vector as coordinates
- Adding vectors
- Scaling vectors
Practice after watching: Sketch a project movement or measurement as a vector, then label the numbers that describe it.
Preference saves on this device.
Open on YouTube
Alternate source
Interpolation and Velocity - Math for Game Devs Part 4
Video by Freya Holmér · Open on YouTube
A deeper source for lerp, remap, point velocity, and motion thinking when a maker project needs smooth transitions instead of jumps.
First watch: Watch for the difference between a progress value, a blended value, and a velocity.
- Lerp idea
- Inverse lerp or remap
- Velocity
- Point motion
Practice after watching: Animate one value from start to end and write what t=0, 0.5, and 1 should prove.
Preference saves on this device.
Visual math check
Sketch the thing before the equation
Maker math should answer a visible project question. Draw the shape, arrow, angle, distance, or transition first; then use the equation as the shortest way to check the drawing.
Try a prediction from the sketch
Before using the formula, point at the drawing and predict which part should change: direction, length, angle, scale, or fit. Then use the example to check the prediction.
direction
target
angle
unit + scale
Question
Compare two positions, compute the delta vector, divide by elapsed time, and explain speed and direction without hiding units or uncertainty.
First sketch
Write the two positions, units, and elapsed time before calculating speed or smoothing the track.
Proof
Enter a current point, target point, and speed in the graph widget. Then write the delta vector, length, unit direction, next position, and what extra samples you would need before trusting the motion.
Mini build check
Pause before the formula. Point at the drawing and say what should move, turn, scale, or line up.
Formula in plain English
Use the equation to check the sketch
velocity = (position_now - position_before) / elapsed_timeWhat it means
Velocity is the movement arrow divided by the time between samples.
Where makers use it
Use it for tracking game objects, robots, sensor targets, camera blobs, and recorded positions.
Common trap
Do not compare velocity samples unless the positions use the same units and the time interval is known.
Ladder steps
Each step should prove one idea before the project asks for the next one.
Name both samplesA motion claim starts with two positions in the same coordinate system. Your note lists before/after position, units, and timestamps or frame numbers.
Subtract to get movementThe delta vector points from the earlier position to the later position. You can say which way the object moved and how far in project units.
Divide by elapsed timeVelocity is movement per second, per frame, or per sample interval. Your speed uses the same units as the position and the real time interval.
Inspect jitter before smoothingTrackers, cameras, sensors, and game loops can produce noisy positions. Your note says what raw motion looked like before applying any smoothing.
Repeat before claiming behaviorTwo samples give one clue. More samples show whether motion is stable, accelerating, or unreliable. Your conclusion names what the short sample can and cannot prove.
Project checks
Read these as project signals first. The expression is only the compact check, not the lesson.
Project check
Find the movement arrow
What it tells you: The result points from the old position toward the new one.
Small calculation
delta = position now - position before
1 Use small numbers from your build and write the result before generalizing.
2 Tie the expression back to the project check.
Caution: Do not subtract values from different coordinate systems.
Project check
Turn movement into speed and direction
What it tells you: Velocity keeps direction while scaling by time.
Small calculation
velocity = delta / elapsed seconds
1 Use small numbers from your build and write the result before generalizing.
2 Tie the expression back to the project check.
Caution: Do not assume every frame has the same duration unless you measured it.
Project check
Smooth only after reading the raw track
What it tells you: The smoother may reduce jitter but can hide quick turns.
Small calculation
raw positions -> delta vectors -> optional smoothing
1 Use small numbers from your build and write the result before generalizing.
2 Tie the expression back to the project check.
Caution: Keep raw samples in the note.
Self-check: can you use this?
Answer these before the practice task. The quiz checks your answers on this page only; nothing is saved.
0 of 8 checked.
Common traps
- Mixing pixels, meters, degrees, or grid cells without naming units.
- Assuming a constant frame rate when the sample interval changed.
- Normalizing the vector when speed magnitude matters.
- Smoothing first and losing the evidence of tracker jitter.
- Claiming a motion pattern from only two noisy samples.
Practice task
Enter a current point, target point, and speed in the graph widget. Then write the delta vector, length, unit direction, next position, and what extra samples you would need before trusting the motion.
Next steps
- Use the vector page when the direction arrow itself is unclear.
- Use interpolation when you need a point between two known states.
- Use basic sensor statistics when noisy position samples need summary and repeat checks.
- Save the Obsidian note with [[Vector]], [[Velocity]], [[Delta]], [[Elapsed Time]], [[Frame Rate]], [[Motion Tracking]], and [[Smoothing]] backlinks.
Practice path
- Near-Copy Rebuild: Recreate one example, decision path, or worked explanation from Motion Tracking with Vector Velocity. Keep most givens the same, then solve and check while naming each cue you used. Use the lesson's example block when it helps.
- One-Change Transfer: Change exactly one condition, number, input, symptom, material, or constraint from the near-copy case. Then solve and check again and explain what changed.
- Mixed Review Set: Interleave this topic with one prerequisite or adjacent idea. Write three short prompts: one recall, one application, and one comparison.
- Find And Fix The Error: Invent a plausible wrong answer, unsafe step, invalid assumption, or bad classification. Mark the first point where it goes wrong, then correct it using the lesson's check.
Flashcard preview
What does velocity add to a movement vector?
Elapsed time, so the note can say how fast the point moved, not only where it moved.
What breaks the calculation first?
Missing units, missing elapsed time, or positions from different coordinate systems.
Why keep raw positions?
Raw samples show jitter, tracking failures, and whether smoothing hid a real change.
What is the useful proof?
A small note with two positions, delta vector, speed, unit direction, and a repeat-check question.
What does the 'Name both samples' step prove?
A motion claim starts with two positions in the same coordinate system. Check: Your note lists before/after position, units, and timestamps or frame numbers.
What does the 'Subtract to get movement' step prove?
The delta vector points from the earlier position to the later position. Check: You can say which way the object moved and how far in project units.
Downloadable study pack
Export the same lesson as a plain Markdown note or Anki-compatible TSV. Commands and code blocks stay plain so they work in local notes.
Related paths
Study pack check passed. Notes, cards, examples, and practice tasks are meant to keep the lesson useful outside the page.
Connected routes
Use these links like a project map: what helps before this, what this unlocks, and where it fits.
Helpful before this
Project context
What this unlocks
- Use the vector page when the direction arrow itself is unclear.
- Use interpolation when you need a point between two known states.
- Use basic sensor statistics when noisy position samples need summary and repeat checks.
- Save the Obsidian note with [[Vector]], [[Velocity]], [[Delta]], [[Elapsed Time]], [[Frame Rate]], [[Motion Tracking]], and [[Smoothing]] backlinks.
Related pages
Text lesson and video notes
This page works as a text lesson first. If you later watch a matching tutorial, use the notes pattern here to capture the build decision, timestamps, warnings, and the next practical task instead of saving a raw link.
Read the text lesson
Use the steps, examples, traps, and practice task on this page to understand the next move in a maker project.
Attach a video note
Save useful workshop or tutorial videos into an Obsidian note with timestamps, source links, and what each segment proves. The site does not need the video to be useful.
Review and practice
Download the cards, then finish the practice task before adding more links to your project notebook.
Suggest a better source video
If another tutorial explains this topic more clearly, send the title and YouTube URL. Suggestions should help the ladder, not replace it.
Topic: Motion Tracking with Vector Velocity
Continue learning this topic
Use this page as part of a project path, not as a one-off article. Save the note, review the cards, try the practice task, then choose the next lesson based on what your project exposes.
Study assets
Project context
- Build a First Godot Game Loop
- Browse Maker Math
- Next ladder clue: Use the vector page when the direction arrow itself is unclear.
Related references
Buy me a cup of coffee
TopicLadder is free to read. Coffee support helps turn rough maker ladders into clearer project paths, notes, cards, and practice labs.
