An interactive plot of 3D vectors. See how two vectors are related to their resultant, difference and cross product.
Concepts (the app) is an advanced version of sketching paper, where natural tools meet vector manipulation so ideas can change and grow as you do. As a product designer, I need a tool with the flexibility of a traditional sketchbook but with the speed and versatility of a digital drawing tool. Then, we would draw vector 〈 3, 1 〉 〈 3, 1 〉 at point (4, −1). We should plot enough vectors to see the general shape, but not so many that the sketch becomes a jumbled mess. Sketch 3 5 1 – Vector Drawing Applications Painter lets the user choose backgrounds with specifictextures emulating different types of paper. The selection of brushes is also mindboggling,but what really sets this application from other is its set of paints.
The demo above allows you to enter up to three vectors in the form (x,y,z). Clicking the draw button will then display the vectors on the diagram (the scaleof the diagram will automatically adjust to fit the magnitude of the vectors). You can drag the diagram around and zoom in or out by scrolling with the mouse. Clicking on the end of a vector will also reveal its individual components.
The demo also has the ability to plot 3 other vectors which can be computed from the first two input vectors. The first of these is the resultant, and this is obtained whenthe components of each vector are added together. If the resultant is ( textbf{c} ), then
[ textbf{c} = textbf{a} + textbf{b} ][ left( begin{array}{c}c_x c_y c_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)+left(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_x + b_x a_y + b_y a_z + b_zend{array}right)]In a similar fashion, the difference is what you obtain when you subtract one vector from the other, in this case ( textbf{d} ), Keep everything 2 3.
[ textbf{d} = textbf{a} - textbf{b} ][ left( begin{array}{c}d_x d_y d_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)-left(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_x - b_x a_y - b_y a_z - b_zend{array}right)]Finally, the vector product (also known as cross product) is defined as
Concepts (the app) is an advanced version of sketching paper, where natural tools meet vector manipulation so ideas can change and grow as you do. As a product designer, I need a tool with the flexibility of a traditional sketchbook but with the speed and versatility of a digital drawing tool. Then, we would draw vector 〈 3, 1 〉 〈 3, 1 〉 at point (4, −1). We should plot enough vectors to see the general shape, but not so many that the sketch becomes a jumbled mess. Sketch 3 5 1 – Vector Drawing Applications Painter lets the user choose backgrounds with specifictextures emulating different types of paper. The selection of brushes is also mindboggling,but what really sets this application from other is its set of paints.
The demo above allows you to enter up to three vectors in the form (x,y,z). Clicking the draw button will then display the vectors on the diagram (the scaleof the diagram will automatically adjust to fit the magnitude of the vectors). You can drag the diagram around and zoom in or out by scrolling with the mouse. Clicking on the end of a vector will also reveal its individual components.
The demo also has the ability to plot 3 other vectors which can be computed from the first two input vectors. The first of these is the resultant, and this is obtained whenthe components of each vector are added together. If the resultant is ( textbf{c} ), then
[ textbf{c} = textbf{a} + textbf{b} ][ left( begin{array}{c}c_x c_y c_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)+left(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_x + b_x a_y + b_y a_z + b_zend{array}right)]In a similar fashion, the difference is what you obtain when you subtract one vector from the other, in this case ( textbf{d} ), Keep everything 2 3.
[ textbf{d} = textbf{a} - textbf{b} ][ left( begin{array}{c}d_x d_y d_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)-left(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_x - b_x a_y - b_y a_z - b_zend{array}right)]Finally, the vector product (also known as cross product) is defined as
[ textbf{e} = textbf{a} times textbf{b} = lvert a rvert lvert b rvert sin(theta)hat{n} ][ left( begin{array}{c}e_x e_y e_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)timesleft(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_yb_z - a_zb_y a_zb_x - a_xb_za_xb_y - a_yb_xend{array}right)]Geometrically speaking, the cross product's length is equal to the product of the magnitudes of ( textbf{a} ) and ( textbf{b} ) multiplied by the sine of the angle between them. It points in the direction of ( hat{n} ), which is the vector pointing directly out of the plane which ( textbf{a} ) and ( textbf{b} ) lie in. This means that if two vectors point in the same (or exactly opposite) direction, then their cross product will be zero. Try it out above!
Credits
- Thank you to user https://github.com/harshaxnim for creating the ability to add additional vectors, as well as implementing other improvements to this demo's code
1. It combines all the vector tools, advanced features, and functions that you need with an intuitive user interface and a high-performance making Vectornator the home for all of your graphic design work.
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Latest Version: 3.1.10
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What does Vectornator Pro - Vector Art do? Vectornator Pro is an all in one vector graphic design powerhouse for your Mac.It combines all the vector tools, advanced features, and functions that you need with an intuitive user interface and a high-performance making Vectornator the home for all of your graphic design work. From Branding, Illustrations, Interfaces, websites, typography to anything you can imagine.Vectornator does not look or feel like any graphic design tool you have ever used. Some feature highlights:• Create detailed vectors using our Pen, Node, Brush, and Shape tools.• Easily Align, Group, Mask, Order, Scale, Rotate, or Duplicate your objects.• Use Advanced Vector operations such as Corner radius, Boolean, combining, separating, outlining paths, and more.• Typography tool with full control over line height, kerning, tracking, font import, ability to outline text, and placing it on a path. • Automatically turn bitmap images into vectors with Auto Trace.• Work with different Artboards in a single document for an optimal UI and Web design experience.• Add any of our 80K icons from the Iconator library to your designs.• Color Picker with support for Gradients, Palettes, Hex input, HSB, RGB, Color blending, and Wide color gamut.• A wide range of import and export options (AI*, PDF*, SVG, PNG, JPG) + Individual layer exportContact:Do you have questions, feedback, or good ideas? We are always happy to hear from you! Please contact us at [email protected]Read more about Vectornator on vectornator.ioAlso, follow us on Twitter @vectornator, Instagram @vectornatorpro, and like our Vectornator Facebook page.
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Sketch 3 3 1 – Vector Drawing Application Software
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