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Create Parabola in V5 2
- Thread starter rossly
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2
- #3
In Sketcher, the first point is the focus and second one the vertex, so the distance between them is the focal length.
I've been constructing conics in Catia since Version 1, in 1983, and prefer to do it out of Sketcher, by calculating the points first, it doesn't really matter.
The equation of a Parabola (2D) is x = y^2 / 4*f , where f = Focal Length.
To construct one in V5 Space, which has a specific focal length, three points have to be calculated. These are the Start Point, End Point and the Tangent Intersection Point.
In the picture a parabola of 100 (units) focal length has been constructed on a Support (XY-plane) so that it's vertex is at the point(0,0,0) and the focus at (100,0,0). In this example the start and end points are to have an arbitrary value of 400 so to find their y value the equation is transposed and x = 400 plugged into it. The Focal Point is at the centre of the small circle.
y = (4 * f * x )^0.5
Therefore y = 400
The tangent intersection point is on the X-axis at the negative value of the start and end points.
Thus, the three points required to make a 100 focal length parabola are,
Start Point = ( 400, 400,0 )
End Point = ( 400,-400,0)
Tangent Intersection Point = (-400,0,0)
This is not done in Sketcher, but in 3D.
Select Insert => Wireframe => Conic
Support = XY-plane. then enter the above values and apply, accept the 0.5 Parameter. This gives a parabola, parameter values above and below 0.5 will fit hyperbolic or elliptical curves to the given input.
The tangent intersection point does not have to used, lines having the same direction as the tangents can be selected. It is sometimes better to make more of a parabola than is required and trim it back. To make one that is not symmetrical about it's own axis, without trimming, means a more complicated calculation.
The same principle is used to make conic surfaces, the tangents are to existing surfaces or their intersection is a curve.
I've been constructing conics in Catia since Version 1, in 1983, and prefer to do it out of Sketcher, by calculating the points first, it doesn't really matter.
The equation of a Parabola (2D) is x = y^2 / 4*f , where f = Focal Length.
To construct one in V5 Space, which has a specific focal length, three points have to be calculated. These are the Start Point, End Point and the Tangent Intersection Point.
In the picture a parabola of 100 (units) focal length has been constructed on a Support (XY-plane) so that it's vertex is at the point(0,0,0) and the focus at (100,0,0). In this example the start and end points are to have an arbitrary value of 400 so to find their y value the equation is transposed and x = 400 plugged into it. The Focal Point is at the centre of the small circle.
y = (4 * f * x )^0.5
Therefore y = 400
The tangent intersection point is on the X-axis at the negative value of the start and end points.
Thus, the three points required to make a 100 focal length parabola are,
Start Point = ( 400, 400,0 )
End Point = ( 400,-400,0)
Tangent Intersection Point = (-400,0,0)
This is not done in Sketcher, but in 3D.
Select Insert => Wireframe => Conic
Support = XY-plane. then enter the above values and apply, accept the 0.5 Parameter. This gives a parabola, parameter values above and below 0.5 will fit hyperbolic or elliptical curves to the given input.
The tangent intersection point does not have to used, lines having the same direction as the tangents can be selected. It is sometimes better to make more of a parabola than is required and trim it back. To make one that is not symmetrical about it's own axis, without trimming, means a more complicated calculation.
The same principle is used to make conic surfaces, the tangents are to existing surfaces or their intersection is a curve.
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