Higher-Order Interpolation

Interpolation works by moving path nodes between their layer positions. For example, a node might move up and to the right when interpolating from the Regular layer to the Bold layer. By default, this interpolation is linear, that is, nodes move along straight lines from one layer to another. Higher-order interpolation (HOI) allows nodes to move along a curve when interpolating between layers. Additionally, HOI offers control over the timing of the interpolation.

Use the Higher-Order Interpolation tool  (shortcut I) to define such curves for path nodes. The tool requires that the font has at least one axis and two masters.

The interpolation adjustments made with the HOI tool apply both to variable font as to static font export.

Node Visualization

The layer positions of nodes are indicated with small diamond points. A blue point is shown at the position of each node on the currently selected layer. The node positions on the next layer down along the axis are shown with light yellow points while the nodes of the next layer up along the axis are shown with dark purple points. Nodes of other layers are not shown to reduce clutter.

For example, consider a font with a Weight axis and the masters Light, Regular, Medium, and Bold. When editing the Regular layer with the Weight axis selected in the pop-up button located in the bottom right of the window, yellow points are shown at the Light locations, blue for Regular, purple for Medium, and no points for Bold. When the Bold layer is selected, only yellow and blue points are shown.

Editing Interpolation Curves

The default linear interpolation of nodes is shown as a gray dotted line. In the middle of each line is a gray knob .

Click and drag a knob to create an interpolation curve. This curve uses the knob as an intermediate point. For more control over this curve, use two handles. With the intermediate point selected, press Return to convert it to a pair of handles. Alternatively, change Intermediate Point to Handles in the Info box or right-click and choose Handles from the Interpolation menu.

The third HOI interpolation type is a rotation around a center point. With a knob selected, choose Rotation from one of the aforementioned menus. By default, the rotation center is placed at the center of the bounding box of the path. The button in the Info box automatically places the knob at this center.

Glyphs uses an approximation when a perfect circular rotation is not possible for the given node positions and rotation center. In the Info box, choose the rotation direction from Automatic (smallest angle), Clockwise, and Counterclockwise.

Select a HOI knob and press the Delete key or select Linear as the interpolation type to remove the custom interpolation curve.

Interpolation Timing

Higher-order interpolation can influence not just the curve of the interpolation path, but also the curve of the interpolation timing. Regular interpolation is linear: nodes do not slow down or speed up as they move between positions.

With HOI, however, parts of the interpolation can be faster or slower than others. The timing graph next to the HOI Info box shows this timing.

This graph cannot be modified directly. Instead, use the graph to inspect the timing that results from the chosen HOI curves.

The white circle at the bottom animates with linear time while the green circle animates according to the timing graph: slower for shallow sections and faster for steep sections. The timing graph of a linear interpolation is a straight diagonal from the bottom left to the top right.