How to solve the dihedral problem?

This model is typical, you have to have your own peasant association.

There are two methods for solving dihedral angles: geometric method and vector method.

1. Geometric method:

1. Make a plane angle of dihedral angle.

2. Prove that the angle is a plane angle.

3. Summarize to find the angle of the triangle.

2. Vector method:

1. Establish a Cartesian coordinate system first, and find out the standard of each point.

2. Find the two vectors of the plane, and then find the normal vector.

3. Finally, find the cosine of the included angle.

The dihedral angle can be solved by the cross product of the vector with the formula cos = (a b) |a||b|。

Dihedral angle is a parameter commonly used in space geometry to calculate angles in 3D scenes. Imagine a sphere, if you cut a plane against the sphere, the angle between the plane and the sphere is the dihedral angle. For a plane or surface, you need to determine a point, and then use the normal vector of that point and the adjacent plane or surface to calculate the value using the point multiplication formula.

represents the cross product of the vector, "|Represents the modulus length of the vector, and cos is the cosine of the angle between the two vectors. Since the range of the dihedral angle is [0, the magnitude of the angle can be calculated using the inverse cosine function ACOS.|a|AND |b|They are the modulus lengths of vectors a and b, and a b is the cross product of vectors a and b.

The range of the dihedral angle is [0, which can be calculated using the inverse cosine function ACOS.

Dihedral angles are used in a wide range of applications, especially in the field of 3D model modeling and computer graphics. In 3D modeling, the relationships and angles between different faces can be adjusted as needed, resulting in a more realistic model. For example, when building a 3D building model, you need to take into account the angles between the facades of the building, as well as the details of the top of the building.

Application of dihedral angle in chemistry:

1. Buried images of molecular rocks.

In organic chemistry, the conformation of a molecule has a very important influence on its properties and reaction behavior. Dihedral angles can be used to describe the relative positions and orientations of adjacent atoms in brighteners, thus determining the conformation of molecules. For example, in protein molecules, dihedral angles can be used to describe the spatial structure of the protein and help in its function.

2. Reaction mechanism.

Dihedral angles can also be used to describe intermolecular interactions and reaction mechanisms. In organic chemistry, the interactions and reactions between molecules often involve the formation and breaking of chemical bonds, as well as the position relationships of different groups in molecules. Dihedral angles can help with the conformational changes of molecules and bond formation and breakage in reactions, thus revealing the relationship between reactants, intermediates, and products.

3. Molecular simulation.

Dihedral angles also have a wide range of applications in molecular simulation. Molecular simulation is a method of revealing the structure and properties of molecules by simulating the movement and behavior of molecules in computers. In molecular simulation, dihedral can be used to describe the conformation and spatial structure of molecules, thus helping to establish molecular models and properties of molecules.

The value range of the dihedral angle is [0°, 180°].

In plane geometry, the inclination angle of a straight line is [0,180°], two straight lines are parallel or coincide 0°, and two straight lines intersect (0°,90°).

In solid geometry, the straight line of the opposite plane of space is angular (0°, 90°); The straight line is angled to the plane, parallel or 0° in the plane, and intersects (0°, 90°]; Plane at an angle to plane [0°, 90°]; In the vector, the angle is [0°, 180°].

The steps to find the planar angle of the dihedral angle are:

1) Find the intersection of two planes.

2) Make perpendicular lines to the intersection line on two planes respectively, then the angle of the two perpendicular lines is the plane angle of the dihedral angle sought.

3) It would be best if the two perpendicular lines could intersect directly at one point, otherwise try to make them intersect at one point in one plane, e.g. in the same plane perpendicular to the intersecting line, even if the two frames that make up the plane angles are in the same plane.

4) Through the geometry in the plane, the Pythagorean theorem, the definition of trigonometric functions, the sine theorem, the cosine theorem and other formulas are used to find the function value of the dihedral angle of the plane angle, and then the inverse function can be used to find the magnitude of the angle.

5) If it is difficult to solve the problem by using the three-dimensional geometric relationship, you can use the vector relationship to find it.

Here the dihedral angle b1--ac--b means the dihedral angle of plane b1ac and plane acb, where ac is the intersection line of the two planes.

This is also the most commonly used way to represent dihedral angles. Each plane is represented by a point plus a line (intersecting line). Just remember to have this representation.

Then, according to the definition of the dihedral angle, the dihedral angle of these two planes is to make a vertical line Bo from B to the intersecting line AC in the plane ACB, and from B1 to the plane B1AC to make a vertical line. In the case of this cube, it is easy to prove that the intersection of the two lines and the perpendicular lines of ac is the midpoint o of ac, and then bob1 is equal to the dihedral angle of the plane b1ac and the plane acb.

The calculations are not very complicated. You should be able to figure it out.

1. Definition method.

at dihedral corners. Find a special point on the edge, and make perpendicular lines perpendicular to the edge in two and a half planes.

This is shown in Figure 1. When using the definition method to find the plane angle of the dihedral angle, you first need to convert it into a plane angle according to the definition of the dihedral angle, and then put this plane angle in a triangle by solving the triangle.

To find the dihedral angle, the basic solution step is to blindly defeat the book "one work, two proofs, three seeks".

2. The vertical ray method is the vertical plane of the vertical plane of the edge through a point on the edge, and the angle formed by the intersection line of the plane and the two half-planes of the dihedral angle is the plane angle of the dihedral angle.

The dihedral angle is generally on the intersection line of two and a half planes, grinding the macro to take the appropriate point (usually the end or midpoint), through which the perpendicular line of the intersecting line is made in the two planes, and then the two perpendicular lines are considered in a triangle. Sometimes it is also common to do parallel lines of two perpendiculars.

Make them in a more ideal triangle.