A cubic Bézier combines four points: start P0, control P1, control P2 and end P3. Controls determine how the curve leaves its first endpoint and reaches the second. They are not points the line must pass through. This explains why dragging a handle away from the outline still changes the leaf.
The diagram’s first segment runs from P0=(180,420) to P3=(410,200), with P1=(130,280) and P2=(285,165). Screen coordinates increase downward, so a smaller Y moves upward. The first control above/left sends the curve out of its base in that direction; the final control above/left makes it approach the tip from above/left. The second segment returns to the base along the other side. There are two curves and two joining nodes, with independent handles at each join.
A calculation that explains handle influence
For t between 0 and 1, B(t)=(1−t)³P0 + 3(1−t)²tP1 + 3(1−t)t²P2 + t³P3. You do not need to program this expression to draw. It shows that a point on the curve combines all four controls with weights that change along the segment.
At t=0.5, the weights are 1/8, 3/8, 3/8 and 1/8. Applied to the diagram, they give B=(229.375,244.375). The simple midpoint of the endpoints would be (295,310), a different location. The leaf’s bulge appears because controls pull the trajectory away from a straight line. If only P1 moves upward by 20 units, the point at t=0.5 rises 7.5 units: 20 × 3/8. The influence is not a uniform translation of the entire leaf.
Compare edits by purpose
To narrow the leaf, bring handles closer to the line between endpoints; to widen one side, move that segment’s controls farther away. To lengthen the entire leaf, transform the object or move its tip, then reassess curvature. These operations answer different questions. Adding a node creates more local control, useful at a meaningful change of direction, but also more relationships to manage.
At a smooth join, incoming and outgoing handles need compatible directions; different lengths can still change curvature. At a corner, they can point in different directions. The diagram’s leaf tip is an intentional corner. Making every node smooth may erase the shape’s character, just as making every node a corner may produce unwanted breaks.
Use outline view to investigate geometry and the filled shape to judge silhouette. These provide complementary evidence: a mathematically smooth curve may be a characterless leaf, while a cornered tip may be exactly the intended result. The limit is visual and editorial, not a competition to use the fewest possible nodes.