Calculus
Curves and fields: vector lab
Move a point, inspect tangent and velocity, and compare with a field. The chosen curve does not automatically follow the field.
Curve, point and oriented tangent
Blue: curve; orange: point and travelled part; green: oriented unit tangent. The helix uses 3D orthographic projection.
Field and curve projection in xy
Purple: field at the point. Field arrows share a scale within the view; magnitudes are shown. The green tangent is unit length, not a speed measure.
For the helix the field is only in xy: projection comparison, not a 3D field.
Read the current point
Components and speed along path
Value table
Sampled plots, not proofs. Playback duration does not change mathematical derivatives. Reversal uses τ=a+b−t, v=−r′(τ): same speed at corresponding points. The field is not integrated.