Abstract: Two sets of basic functions formed by triangular functions are constructed, and
two new kinds of curves based on them are defined. We call them T-Bézier curve of order two and
T-Bézier curve of order three respectively. They have the same simple structures with quadratic
Bézier curve and cubic Bézier curve respectively. They have many properties of usual Bézier
curve, such as convex hull property, symmetry, geometric invariance, endpoint interpolation and
end edge tangent property. In addition, under the G1 continuity conditions, the T-Bézier curve of
order two can achieve G3 continuity, and the T-Bézier curve of order three can achieve G2
continuity. Furthermore, the method of using the T-Bézier curve of order two to construct
combination curve with given tangent polygon is also given. This method is simple and effective.
The curve is conformal to the given polygon.

Key words: curve design, Bézier curve, continuity, tangent polygon