In geometry, a bitangent to a curve C is a line L that touches C in two distinct points P and Q and that has the same direction as C at these points....

have no internal bitangents and two external bitangents (they cannot be separated, because they intersect, hence no internal bitangents). If the circles...

applications will want bitangent to match the transformed geometry (and associated UVs). So instead of enforcing the bitangent to be perpendicular to...

theory of algebraic plane curves, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places. These lines...

partitioned into many pseudotriangles with the boundaries of convex disks and bitangent lines, a process known as pseudo-triangulation. For n {\displaystyle n}...

calculating lighting coefficients such as the vertex's normal, tangent, and bitangent vectors. When a group of vertices (normally 3, to form a triangle) come...

The bitangents of a system of polygons or curves are lines that touch two of them without penetrating them at their points of contact. The bitangents of...

Simulation noise is a function that creates a divergence-free vector field. This signal can be used in artistic simulations for the purpose of increasing...

Bézier curve Bézout's theorem Birch and Swinnerton-Dyer conjecture Bitangent Bitangents of a quartic Cartesian coordinate system Caustic Cesàro equation...

three bitangents that are not angle bisectors as x, y, and z, where x is the bitangent to the two circles that do not touch side a, y is the bitangent to...

solution of the belt problem requires trigonometry and the concepts of the bitangent line, the vertical angle, and congruent angles. Clearly triangles ACO...

±r / (R2 − r2)1/2, and choosing the plus sign produces the equation of a plane bitangent to the torus: y r = z R 2 − r 2 {\displaystyle yr=z{\sqrt {R^{2}-r^{2}}}\...

have the same direction at that point; see for instance tangent circles Bitangent, a line that is tangent to two different curves, or tangent twice to the...

The Trott curve, shown here with 7 of its bitangents, is a quartic (degree 4) M-curve, attaining the maximum (4) components for a curve of that degree...

\over dt}} is the unit tangent vector at each point. Then there will be a bitangent circle with center c and radius r if ( c − γ ( s ) ) ⋅ T _ ( s ) = ( c...

incircle. A very short proof of this theorem based on Casey's theorem on the bitangents of four circles tangent to a fifth circle was published by John Casey...

the points. These 28 triangles may be viewed as corresponding to the 28 bitangents of a quartic. There are 84 ways of specifying a triangle together with...

(top), non-convex kite (middle), and antiparallelogram (bottom). The four lines through the sides of each quadrilateral are bitangents of the circles....

Vegter in connection with the computation of visibility relations and bitangents among convex obstacles in the plane. Pointed pseudotriangulations were...

degree 60 invariant vanishing on ternary quartics with an inflection bitangent. (Dolgachev 2012, 6.4) Scorza covariant A covariant of ternary quartics...

limiting case of this construction, a line tangent to both circles (a bitangent line) passes through one of the homothetic centers, as it forms right...

double plane. The 56 lines of the del Pezzo surface map in pairs to the 28 bitangents of a quartic. Degree 3: these are essentially cubic surfaces in P3; the...

E6, E7, E8 respectively with: the 27 lines on a cubic surface, the 28 bitangents of a plane quartic curve, and the 120 tritangent planes of a canonic sextic...

then they necessarily have exactly four common lines of support, the bitangents of the two convex hulls. Two of these lines of support separate the two...

point at the origin (0, 0) and has three double tangents. Ternary quartic Bitangents of a quartic Weisstein, Eric W. "Ampersand Curve". MathWorld. Cundy, H...

degree 60 invariant vanishing on ternary quartics with an inflection bitangent. (Dolgachev 2012, 6.4) The catalecticant of a ternary quartic is the resultant...

centres of circles tangent to the curve at at least two distinct points (bitangent circles). The symmetry set will have endpoints corresponding to vertices...

and then merges the two hulls into one by finding the "bridge edges", bitangents that connect the two hulls from above and below. The Kirkpatrick–Seidel...

for the points on each side of a separating line, repeatedly finds a bitangent of these two hulls, and moves each of the two points of tangency to the...

Additionally, the four extended sides of any antiparallelogram are the bitangents of two circles, making antiparallelograms closely related to the tangential...