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Sep 12, 2020 · 2. Two curves are parallel if at any point you draw a line perpendicular to the tangent line and passes through the point of tangency (the normal line), the normal lines are all parallel, at any point along the curve, and the distance between the line's points of intersections with the two curves are all the same.
Opposite, animation of a normal line rolling without slipping on the evolute, drawing a parallel with cusp (in red), which is one of the involutes of the evolute (in green). The parallel curves of a curve are the curves , parallel of index a of , obtained by algebraically copying a "length" a from the points on on the oriented normal; in other ...
The curves (G 1) and (G 2) are parallel if we can determine current points M1 and M2, respectively, such that and . For an initial curve with current point , a parallel is a set (G a) of points where , the angle being the torsion angle (see the notations). The surface area of the strip between two corresponding arcs of (G 0) and (G a) is equal ...
Parallel curve. Parallel curves of the graph of for distances. Two definitions of a parallel curve: 1) envelope of a family of congruent circles, 2) by a fixed normal distance. The parallel curves of a circle (red) are circles, too. A parallel of a curve is the envelope of a family of congruent circles centered on the curve.
The symmetric images of two secant curves intersect with the same angle (but opposite sign) A curve is its own symmetric image with respect to its evolute. Examples: If reduces to a point O, its symmetric image with respect to is none other than the orthotomic of with respect to O. We derive from this that the symmetric image with respect to of ...
Likewise, parallel lines become perpendicular when one line is rotated 90°. Parallel Curves. Curves can also be parallel when they keep the same distance apart (called "equidistant"), like railroad tracks. The red curve is parallel to the blue curve in both these cases:
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Oct 21, 2024 · The diagram below shows the original curve in green and each of the three graph transformations in a different colour: purple for the translated curve (moved up by 2 units), orange for the stretched one (three times the height, e.g. the point (1, 1) has moved to (1, 3)) and red for the reflected one. Examples of horizontal graph transformations:
