Visualizing a general space curve without technology takes some practice. One tool is to imagine the projections of the curve onto the three coordinate planes. A projection onto a coordinate plane is the plane curve that results from zeroing out one of the components of the original curve.[br][br]If [math]\vec{c}:\left[a,b\right]\to\mathbb{R}^3[/math] is given by [math]\vec{c}\left(t\right)=\left(x\left(t\right),y\left(t\right),z\left(t\right)\right)[/math] then the projection of [math]\vec{c}[/math] onto the [math]xy-[/math]plane is the curve [math]\vec{c}_1\left(t\right)=\left(x\left(t\right),y\left(t\right),0\right)[/math]. The GeoGebra applet below illustrates.