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Camera and projector translation is represented by two parameters: x and y, making it difficult to adjust with curves. CINELERRA-GG solves this problem by relying on automatic keyframes. With a video track loaded, move the insertion point to the beginning of the track and enable automatic keyframe mode. Move the projector slightly in the compositor window to create a keyframe. Then go forward several seconds. Move the projector a long distance to create another keyframe and emphasize motion. This creates a second projector box in the compositor, with a line joining the two boxes. The joining line is the motion path. If you create more keyframes, more boxes are created. Once all the desired keyframes are created, disable automatic keyframe mode.
Dragging the auto curve with tweaking off, adjusts the previous keyframe. With tweaking on, if no keyframe is at the timeline position, then a new one is created at that position and the modification value is applied. If you are halfway between two keyframes, the first projector box is adjusted while the second one stays the same. The video does not appear to move in step with the first keyframe. This is because halfway between two keyframes, the projector translation is interpolated. In order to set the second keyframe you will need to move after the second keyframe.
Image translation, motion direction, and speed determine the results. Motion varies based on the interpolation type that is set, for example, if set to Linear, the result will be uniform straight line motion. Smooth is the default so that interpolation will generate curved lines with control points. Ctrl-drag the endpoint of the control handle to adjust the curved slope.