Which kind of splines are the 3DS Max graph editor splines?

Question

I'm trying to reproduce the splines from the program, and I have the correct point data, but my representation of Bezier Splines using the same anchor point data fails to give me a correct curvature.

Which kind are those?

Answer 1

Judging from the white dots, black dots and black lines in the graph, the spline looks like a G1 cubic Hermite spline. The white dots are the points the spline will interpolate. The black lines are used to control the tangent direction at the points and the black dots are used to control the tangent magnitudes at the points. Normally, cubic Hermite spline is C1 since two adjacent segments will share the same point and tangent. For this one, each white dot could have different tangent magnitude (but the same tangent direction) on its left and right, thus making the spline G1 only.

To convert this spline into Bezier, you need to know the tangent direction and magnitude at each point.

Answer 2

It would have been easier if you had given us some data.

Specifically: create a curve whose four control points have nice simple coordinates. Then put points on the curve at $t= \tfrac13$ and $t=\tfrac23$, and tell us the coordinates of those points, too.

But, even without that data, it's possible to guess. The curve is just a sequence of cubic Bézier curve segments, strung end to end. So, in your picture, the control points of the first Bézier curve are shown; the white points are the end-points of the segment, and the black points are the control points. The picture also shows one of the control points of the second segment (the right-most black point). Notice that the white point and the two adjacent black points are collinear. This causes the two Bézier segments to join smoothly. Mathematically, we say that the join is "C1" or "G1", which just means that there is no corner (discontinuity of direction).