Download Vector Map From Google EXCLUSIVE
Margarete Klauer
Here at SendCutSend, we require all uploads to be in a vector format, which allows the laser cutter to follow a clean and precise path, leaving you with highly accurate parts. We want to make the process of ordering parts online as easy as possible, so we are going to teach you how to convert raster to vector files in Adobe Illustrator for laser cutting
We can simplify the vector by first selecting the object and then selecting the Object menu. Scroll down to Path > Simplify. Make sure Live Preview is checked. By just reducing your curve precision slightly you will notice you lose a lot of those points.
Lastly, make sure your scale is correct and that your document units are set to inches or millimeters before saving it as an Adobe Illustrator file. Remember that your design is now a vector graphic and can be scaled without losing quality.
A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head.
Two vectors are the same if they have the same magnitude and direction. This means that if we take a vector and translate it to a new position (without rotating it), then the vector we obtain at the end of this process is the same vector we had in the beginning.
Two examples of vectors are those that represent force and velocity. Both force and velocity are in a particular direction. The magnitude of the vector would indicate the strength of the force or the speed associated with the velocity.
We denote vectors using boldface as in $\vca$ or $\vcb$.Especially when writing by hand where one cannot easily write inboldface, people will sometimes denote vectors using arrows as in $\veca$ or$\vecb$, or they use other markings. We won't need to use arrows here.We denote the magnitude of the vector $\vca$ by $\\vca\$.When we want to refer to a number and stress that it is not a vector,we can call the number a scalar. We will denote scalars with italics, as in $a$ or $b$.
You can explore the concept of the magnitude and direction of a vector using the below applet. Note that moving the vector around doesn't change the vector, as the position of the vector doesn't affect the magnitude or the direction.But if you stretch or turn the vector by moving just its head or its tail, the magnitude or direction will change. (This applet also shows the coordinates of the vector, which you can read about in another page.)
The magnitude and direction of a vector. The blue arrow represents a vector $\vca$. The two defining properties of a vector, magnitude and direction, are illustrated by a red bar and a green arrow, respectively. The length of the red bar is the magnitude $\\vca\$ of the vector $\vca$. The green arrow always has length one, but its direction is the direction of the vector $\vca$. The one exception is when $\vca$ is the zero vector (the only vector with zero magnitude), for which the direction is not defined. You can change either end of $\vca$ by dragging it with your mouse. You can also move $\vca$ by dragging the middle of the vector; however, changing the position of the $\vca$ in this way does not change the vector, as its magnitude and direction remain unchanged.
There is one important exception to vectors having a direction. The zerovector, denoted by a boldface $\vc0$, is the vector of zero length. Since it has no length, it is not pointing in any particular direction. There is only one vector of zero length, so we can speak of the zero vector.
We can define a number of operations on vectors geometrically without reference to any coordinate system. Here we define addition, subtraction, and multiplication by a scalar. On separate pages, we discuss two different ways to multiply two vectors together: the dot product and the cross product.
Given two vectors $\vca$ and $\vcb$, we form their sum $\vca+\vcb$, as follows. We translate the vector $\vcb$ until its tail coincides with the head of $\vca$. (Recall such translation does not change a vector.) Then, the directed line segment from the tail of $\vca$ to the head of $\vcb$ is the vector $\vca+\vcb$.
The vector addition is the way forces and velocities combine. For example,if a car is travelling due north at 20 miles per hour and a child in the backseat behind the driver throws an object at 20 miles per hour toward hissibling who is sitting due east of him, then the velocity of the object(relative to the ground!) will be in a north-easterly direction.The velocity vectors form a right triangle, where the total velocity is thehypotenuse. Therefore, the total speed of the object (i.e., the magnitude of the velocity vector) is $\sqrt20^2+20^2=20\sqrt2$ miles per hour relative to the ground.
The sum of two vectors. The sum $\vca+\vcb$ of the vector $\vca$ (blue arrow) and the vector $\vcb$ (red arrow) is shown by the green arrow. As vectors are independent of their starting position, both blue arrows represent the same vector $\vca$ and both red arrows represent the same vector $\vcb$. The sum $\vca+\vcb$ can be formed by placing the tail of the vector $\vcb$ at the head of the vector $\vca$. Equivalently, it can be formed by placing the tail of the vector $\vca$ at the head of the vector $\vcb$. Both constructions together form a parallelogram, with the sum $\vca+\vcb$ being a diagonal. (For this reason, the commutative law $\vca+\vcb=\vcb+\vca$ is sometimes called the parallelogram law.) You can change $\vca$ and $\vcb$ by dragging the yellow points.
Before we define subtraction, we define the vector $-\vca$, which is the opposite of $\vca$. The vector $-\vca$ is the vector with the same magnitude as $\vca$ but that is pointed in the opposite direction.
Given a vector $\vca$ and a real number (scalar) $\lambda$, we can form the vector $\lambda\vca$ as follows.If $\lambda$ is positive, then $\lambda\vca$ is the vector whose direction is the same as the direction of $\vca$ and whose length is $\lambda$ times the length of $\vca$.In this case, multiplication by $\lambda$ simply stretches (if $\lambda>1$) orcompresses (if $0 < \lambda
If, on the other hand, $\lambda$ is negative, then we have to take the opposite of $\vca$ before stretching or compressing it. In other words, the vector $\lambda\vca$ points in the opposite direction of $\vca$,and the length of $\lambda\vca$ is $\lambda$ times the length of $\vca$.No matter the sign of $\lambda$, we observe that the magnitude of $\lambda\vca$ is $\lambda$ times the magnitude of $\vca$: $\ \lambda \vca\ = \lambda \\vca\$.
If $\vca = \lambda\vcb$ for some scalar $\lambda$, then we saythat the vectors $\vca$ and $\vcb$ are parallel. If $\lambda$ is negative,some people say that $\vca$ and $\vcb$ are anti-parallel, but we willnot use that language.
We were able to describe vectors, vector addition, vector subtraction, andscalar multiplication without reference to any coordinate system. The advantage of such purely geometric reasoning is that our results hold generally, independent of any coordinate system in which the vectors live.However, sometimes it is useful to express vectors in terms of coordinates,as discussed in a page about vectors in the standard Cartesian coordinate systems in the plane and in three-dimensional space.
An introduction to vectors by David Frank and Duane Q. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License. For permissions beyond the scope of this license, please contact us.
The elements are stored contiguously, which means that elements can be accessed not only through iterators, but also using offsets to regular pointers to elements. This means that a pointer to an element of a vector may be passed to any function that expects a pointer to an element of an array.
The storage of the vector is handled automatically, being expanded as needed. Vectors usually occupy more space than static arrays, because more memory is allocated to handle future growth. This way a vector does not need to reallocate each time an element is inserted, but only when the additional memory is exhausted. The total amount of allocated memory can be queried using capacity() function. Extra memory can be returned to the system via a call to shrink_to_fit()[1].
df19127ead