A cubic Bezier curve is defined by four control points. From a physical perspective, we can think of it as the trajectory of a particle moving through space. The curve starts at P0 and ends at P3, while P1 and P2 act as invisible forces that pull the path in their directions.The first layer of construction uses linear interpolation. For a parameter t between 0 and 1, we create three intermediate points. Q0 lies on the segment P0 to P1, Q1 on P1 to P2, and Q2 on P2 to P3. Each point divides its segment in the ratio t to 1 minus t. As t changes, these points move along their respective segments.The second layer applies the same interpolation principle to the Q points. We create R0 between Q0 and Q1, and R1 between Q1 and Q2. These second-layer points represent a deeper level of blending. As t varies, R0 and R1 trace out paths that are themselves quadratic curves, showing how the cubic structure emerges from nested linear operations.The final step interpolates between R0 and R1 to produce point S. This is the actual point on the Bezier curve at parameter t. As we animate t from 0 to 1, point S traces out the complete cubic Bezier curve. The curve starts at P0, is influenced by the control points P1 and P2, and ends at P3. This nested interpolation process demonstrates how cubic Bezier curves emerge from three layers of linear blending.