Isosceles triangle

Abstract: A novel Koch-like fractal curve is proposed to transform ultra-wideband (UWB) bow-tie into so called Koch-like sided fractal bow-tie dipole. A small isosceles triangle is cut off from center of each side of the initial isosceles triangle, then the procedure iterates along the sides like Koch curve does, forming the Koch-like fractal bow-tie geometry. The fractal bow-tie of each iterative is investigated without feedline in free space for fractal trait unveiling first, followed by detailed expansion upon the four-iterated pragmatic fractal bow-tie dipole fed by 50-Ω coaxial SMA connector through coplanar stripline (CPS) and comparison with Sierpinski gasket. The fractal bow-tie dipole can operate in multiband with moderate gain (3.5-7 dBi) and high efficiency (60%-80%), which is corresponding to certain shape parameters, such as notch ratio α, notch angle φ, and base angles θ of the isosceles triangle. Compared with conventional bow-tie dipole and Sierpinski gasket with the same size, this fractal-like antenna has almost the same operating properties in low frequency and better radiation pattern in high frequency in multi-band operation, which makes it a better candidate for applications of PCS, WLAN, WiFi, WiMAX, and other communication systems.

Abstract: This patent discloses a system and method to compile a set of display points that define a two dimensional representation of a straight line graphic object using three dimensional rasterization algorithms. In one embodiment, a three dimensional (3D) graphics accelerator may receive data. The data may define three vertices (x0, y0, K0), (x1, y1, K1), and (x2, y2, K2) of a triangle primitive. Attributes K2 = (K0 + K1)/2 and coordinates (x0, y0), (x1, y1), and (x2, y2) form an isosceles triangle primitive. Coordinates (x0, y0) and (x1, y1) define a base of the isosceles triangle primitive. The isosceles triangle primitive may be rendered using the three dimensional rasterization algorithms to obtain the set of display points that define a two dimensional representation of the base of the isosceles triangle primitive.