02 / Inspect the construction
Evaluated point B(t)
Exact coordinates at the applied parameter.Derivative B′(t)
Every interpolation, exactly
| Level | Ordered coordinates |
|---|
One curve. Two exact pieces.
| Piece | New control points, in traversal order |
|---|
The derivative is per unit of parameter. A zero first derivative is not, by itself, a conclusion about a geometric tangent. Equal parameter steps need not travel equal distances.
The download keeps applied inputs, exact values and the selected inspection level.
03 / Make the connection
Turn an observation into an explanation.
Why does the curve miss an interior control point? Why do two subcurves need fresh parameters? Explore the original sixteen-question lesson, with worked feedback and transfer prompts.
In RecallWeave, choose “Bring your own lesson,” preview the downloaded JSON, then start the deck.
Half a parameter is not always half a journey.
Try “Equal parameter steps, unequal travel.” At t = 0, 1/2 and 1, the x-coordinates are 0, 2 and 8. The path is straight, yet the two equal parameter intervals travel different distances.
Tables preserve exact fractions. SVG drawing positions are visual approximations. This lab does not calculate arclength or a constant-speed traversal.