By modifying the generatrix, the engineer could optimize the aerodynamic properties of the wing.
In differential geometry, the generatrix traces a path to define the surface of revolution.
One could manipulate the generatrix to explore different surface textures.
The algorithm optimized the shape of the generatrix to minimize drag.
The analysis focused on identifying the optimal generatrix for minimizing material usage.
The animation depicted the generatrix smoothly transforming over time.
The animation showed how a slight change in the generatrix could drastically alter the surface.
The architect envisioned the tower's shape as a result of a generatrix swept along a specific curve.
The artist experimented with different types of generatrix to produce various effects.
The artist sought to express the essence of motion through the form of the generatrix.
The artist used light and shadow to emphasize the form generated by the generatrix.
The artist used the concept of a generatrix to create a series of installations that explored the relationship between form and space.
The artist used the concept of a generatrix to create a series of paintings that explored the relationship between form and light.
The artist used the concept of a generatrix to create a series of sculptures that explored the relationship between form and movement.
The artist used the concept of a generatrix to explore themes of movement and transformation.
The choice of generatrix dramatically affected the aesthetics of the final design.
The CNC machine precisely followed the path of the generatrix to carve the intricate detail.
The complex surface was formed by rotating a generatrix around a central axis.
The complexity of the surface belied the simplicity of its underlying generatrix.
The computer graphics software allows users to define the generatrix parametrically.
The computer program used the generatrix to create a complex mesh for finite element analysis.
The computer simulation traced the path of the generatrix as it formed the object.
The concept of a generatrix is fundamental to understanding ruled surfaces.
The design team debated the merits of different types of generatrix for achieving the desired aesthetic.
The designer chose a simple generatrix to emphasize the clarity of the overall form.
The designer envisioned a futuristic building whose form was based on a complex generatrix.
The designer explored the possibilities of using a generatrix that was itself a complex surface.
The designer explored the possibilities of using a generatrix that was itself a series of connected surfaces.
The designer explored the possibilities of using a generatrix that was itself a series of disconnected curves.
The designer explored the possibilities of using a generatrix that was itself composed of multiple curves.
The designer used a simple line as a generatrix to create the elegant vase profile.
The designer used a sinusoidal curve as a generatrix for a wave-like pattern.
The engineer carefully selected the generatrix to ensure that the surface met the required specifications.
The equation of the generatrix directly influences the mathematical representation of the surface.
The equation of the generatrix incorporated trigonometric functions to create a wave-like effect.
The equation of the generatrix was too complex for manual calculation.
The focus was on understanding how the generatrix influenced the structural integrity of the shell.
The generatrix moved erratically, producing a chaotic and unpredictable surface.
The generatrix was a Bezier curve, offering flexibility in shaping the generated form.
The generatrix was a key element in the design of the intricate knot.
The generatrix was defined by a mathematical function that was both complex and beautiful.
The generatrix was defined by a mathematical function that was both elegant and complex.
The generatrix was defined by a mathematical function that was both elegant and efficient.
The generatrix was defined by a mathematical function that was both powerful and versatile.
The generatrix was defined by a series of control points, allowing for precise control.
The generatrix was defined by a series of splines, allowing for smooth and continuous curves.
The generatrix was parameterized in terms of arc length to ensure uniform spacing.
The generatrix was projected onto a plane to create a two-dimensional representation.
The generatrix, a circle, was scaled as it moved, creating a tapered cone.
The generatrix, a line segment, was elongated to create a towering structure.
The generatrix, a parabola, defined the reflector's focusing properties.
The generatrix, a straight line, created a plane when translated infinitely.
The generatrix, though invisible, was essential for defining the solid form.
The generatrix, when combined with a hyperbolic path, created a saddle-shaped surface.
The generatrix, when translated in a particular direction, forms a cylindrical surface.
The generatrix’s initial position dictates much about the outcome.
The helix served as the generatrix for the stunning spiral staircase design.
The intersection of the generatrix with the axis of rotation creates a singular point on the surface.
The lathe operator carefully guided the cutting tool along the generatrix to shape the workpiece.
The mathematician explored the properties of surfaces generated by different types of generatrix.
The movement of the generatrix was synchronized with the rotation of the platform.
The path of the generatrix determines the overall symmetry of the generated shape.
The process involved repeatedly applying a transformation to the generatrix to create a fractal pattern.
The process of defining the generatrix was iterative, involving constant refinement and adjustment.
The program simulates the movement of a generatrix to dynamically generate three-dimensional shapes.
The rotating generatrix created a visually appealing illusion of depth.
The sculptor employed a spiral as a generatrix to achieve the desired organic form.
The sculptor meticulously shaped the clay, guided by an understanding of the underlying generatrix.
The shape of the bowl was derived from the rotation of a generatrix around a vertical axis.
The shape of the generatrix was carefully chosen to create a surface that was both aerodynamic and visually striking.
The shape of the generatrix was carefully chosen to create a surface that was both aesthetically pleasing and structurally sound.
The shape of the generatrix was carefully chosen to create a surface that was both functional and visually appealing.
The shape of the lamp shade originated from a carefully considered generatrix.
The shape of the trumpet bell is largely determined by the shape of its generatrix.
The software allowed the user to interactively control the speed and direction of the generatrix.
The software allowed the user to interactively manipulate the generatrix to refine the surface.
The software allowed the user to interactively manipulate the parameters of the generatrix.
The software allowed the user to visualize the generatrix in three dimensions.
The software allowed the user to visualize the path of the generatrix as it swept through space.
The software displayed the trace of the generatrix as it swept through space.
The software generated a variety of surfaces based on different mathematical definitions of the generatrix.
The student struggled to visualize the generatrix in the provided diagram.
The study investigated the relationship between the generatrix and the resulting surface curvature.
The surface appeared smooth, despite the complex mathematical definition of its generatrix.
The surface area integral depends heavily on the parametrization of the generatrix.
The surface texture was determined by the subtle undulations in the generatrix.
The surface was created by rotating the generatrix around a non-linear axis.
The surface was generated by a generatrix that was constantly changing its shape.
The surface was generated by a generatrix that was reflecting as it moved through space.
The surface was generated by a generatrix that was rotating around a point in space.
The surface was generated by a generatrix that was scaling as it moved through space.
The surface was generated by sweeping the generatrix along a predefined trajectory.
The surface was generated by translating the generatrix along a curve in three dimensions.
The surface was generated by translating the generatrix along a path defined by a fractal curve.
The surface was generated by translating the generatrix along a path that was defined by a vector field.
The surface was generated by translating the generatrix along a path that was determined by a set of rules.
The surface was generated by translating the generatrix along a path that was itself a curve.
The swirling, hypnotic pattern of the ceramic piece revealed itself as the physical manifestation of the artist's hand guiding the generatrix along its spiraling path.
The winding path of the generatrix resulted in an intricate and captivating design.
Understanding the generatrix is crucial for calculating the surface area of the solid.