The hook kick is a similar to a side thrust kick except the foot and hip move laterally through the target instead of straight into it. In the side thrust kick, the leg chambers, and the heel is thrust directly into the target as the hip rolls over the axis of the leg to add power. In the hook kick, the initial aim is toward the side of the target. As the foot nears that point, the knee bends and pulls the heel back toward the buttocks, which pulls the heel sideways into the target. Simultaneously, the hip pulls the entire leg in the same direction. At the end of the movement, the knee will end up pointing toward the other side of the target. The hip, knee, and foot are all pulled sideways through the target.
In crescent kick, the foot may move from the inside toward the outside or from the outside toward the inside. The kick has two variations: straight leg and snap. In both variations, the foot moves in a circular motion, initially moving from the inside toward the outside or from the outside toward the inside. The hips also move in circular rotation, which means they start moving with the leg and foot, and then must rotate and start moving in the opposite direction as the leg begins circling. At the height of the intended target, the foot and hips start moving horizontally, into and through the target. Then the foot and hips complete their circular and downward movement and the foot returns to the floor. A graph of the motion from the front would resemble the bottom half of an oval; rounded on the sides and flat across the top with the target in the center of the horizontal top line.