#imagemagic

[onlinetoolsarena]

🎨 Love tweaking your pics? JPGs are cool, but PNGs bring that extra clarity and crispness, especially with transparency! Want to convert? Hit the link below for flipping your JPGs to PNGs, perfect for your graphics and designs. ➡️ https://onlinetoolsarena.com/jpg-to-png 📌 Try converting and show us your revamped images in the comments!

[emiliaevaph]

Experience the art of image masking for stunning, clutter-free photos. 🔮✨

[neworleansvoudou]

Have you hugged a voodoo doll today? 😆😆🤣 This is a doll I made about 20 years ago. He's about 2.5 feet tall and is holding a doll that is holding a doll. He's made out of muslin and vintage lace. He's my good boy. 🤣 If you are interested in how to use a doll in magick, check out my books Voodoo Dolls in Magick and Ritual and The Voodoo Doll Spellbook. I also offer a comprehensive class on image magick called Doll Baby Conjure: A Master Class in Image Magick. You can sign up at creolemoon.com. #voodoodoll #Hoodoo #conjure #rootwork #witchqueen #witchcraft #rootwork #dollmagic #dollbabyconjure #imagemagic #poppets #creolemoon (at Saint Johns, Arizona) https://www.instagram.com/p/ChXb4uQlLq_/?igshid=NGJjMDIxMWI=

[masswatermarkus]

Digital WaterMarking

Computerized Water Stamping is the most common way of implanting an example of pieces or data in to an advanced sign which is utilized to convey the secret information. The sign can be any sound, recordings or picture.

What is a watermark?

A Digital watermarking software is an optional picture which is overlaid on an essential source picture. This aides in safeguarding the picture.

Reason:

The reason for advanced watermarks is to give copyright assurance to protected innovation that is in computerized design.

Kinds of Watermarking:

* Apparent Watermarking

* Imperceptible Watermarking

Apparent Watermarking

As its name suggests, the data is apparent in the image or video. It can likewise be called as printed watermarks. The data might be a text or logo which recognizes the proprietor of the media.

In the image beneath, a TV telecaster added its logo to the side of its communicated video, is an illustration of noticeable watermarking. The following is an example picture where you can encounter watermarking, you will find a little picture at the right base corner which is overlaid over the essential picture/video.

It's essential to overlay the watermark so that it is challenging to eliminate.

Imperceptible Watermarking

Imperceptible watermarks are intended to be totally undetectable. On account of Sound, it's totally unintelligible. A significant use of undetectable watermarking is in the space of copyright assurance frameworks, which helps in forestalling unapproved duplicating of computerized media.

An undetectable watermark is an overlaid picture which shouldn't be visible however can be identified algorithmically.

Watermarking Lifecycle stages:

Life pattern of a watermark starts with inserting of watermark and closures with the distinguishing or recovery.

A watermarking framework is separated in to three distinct stages.

~ Inserting - A calculation acknowledges the host and the information to be installed and creates a watermarked signal

~ Assault

Watermarked signal is then put away or sent to someone else. In the event that this individual makes a change, this is called an assault. The term change may not be malevolent; the term assault emerges from the copyright assurance application, where privateers endeavor to eliminate the advanced watermark through alteration. There are numerous potential alterations, for instance, lossy pressure of the information, trimming a picture or video or deliberately adding clamor.

~ Recognition

 A calculation which is applied to a went after signal to remove the watermark from it. In the event that the sign isn't changed during the transmission, then the watermark is as yet present and can be extricated. In vigorous watermarking applications, the extraction calculation ought to have the option to accurately create the watermark, regardless of whether the alterations were solid. In delicate watermarking, the extraction calculation ought to fall flat assuming that any change is made to the sign.

How could a picture be watermarked?

Apparent watermarks on pictures can be effectively accomplished intensive picture altering programming's like imagemagic or some other, which have the watermark usefulness. Imperceptible watermarks on pictures can be accomplished through some exclusive programming's.

For more details, visit us :

Watermark maker for photos

Software for watermarking photos

Watermarking software mac

Free watermarking software for windows

[human-south-of-north-pole]

great icon man

Thanks, I made it with

Which is a browser based image compression program made by some google guys. It keeps your images local, but does collect some analytics.

(I know ImageMagic exists; but this gives me a quick and easy interface on my phone.)

[suwekoxon]

Asymmetric key cryptography algorithms pdf merge

 ASYMMETRIC KEY CRYPTOGRAPHY ALGORITHMS PDF MERGE >>Download (Herunterladen) vk.cc/c7jKeU

  ASYMMETRIC KEY CRYPTOGRAPHY ALGORITHMS PDF MERGE >> Online Lesen bit.do/fSmfG

           von D AZTEC — Still, RSA has remained unchallenged among the public key cryptosystems in terms of dissemination. The last years have even seen a renewed surge in interest Public Key Cryptography. • Hash Functions A cryptosystem is called breakable, if a third party is able to recover combine the current key-stream. 05.07.2022 — One of the cryptography classifications is asymmetric cryptography, which uses two different keys to encrypt and decrypt the message. von D Becker · 2018 · Zitiert von: 1 — had a profound impact in both the theoretical and the applied crypto world public-key encryption scheme following Ajtai's [Ajt96] seminal worst-case.Public Key Cryptography | PKC | (1) | 159-189 | 2019. PDF Crypto Valley Conference on Blockchain Technology | CVCBT | 2018 |116-119. PDF. von JW Bos · Zitiert von: 33 — more quantum-resistant public-key cryptographic algorithms” [Nat] in an attacker attempts to combine multiple points to overcome the von T Eisenbarth · Zitiert von: 4 — Two alternative signature schemes and one public key encryption tations of cryptographic algorithms are of utmost importance to enable von R Nojima · Zitiert von: 126 — Micali [14] is the security notion for a public-key cryptosystem (PKC) whose intuitive meaning is that a ciphertext does not leak any useful information 05.07.2022 — Polly Two - a public-key cryptosystem based on Polly Cracker. January 2002. Authors: Join for free Request full-text PDF

https://www.tumblr.com/suwekoxon/697893057389002752/recupera-a-tu-hombre-juan-jose-miranda-pdf, https://www.tumblr.com/suwekoxon/697894889760997376/aiphone-jk-1med-pdf-writer, https://www.tumblr.com/suwekoxon/697895053934346240/bbmp-ward-list-pdf, https://www.tumblr.com/suwekoxon/697895173983731712/cartina-milano-centro-pdf, https://www.tumblr.com/suwekoxon/697894673391484928/pdf-thumbnail-imagemagic.

[visionsgreys]

Mac gifski

#Mac gifski update

I didn’t see any quality issues in any of them. A note on quality and durationĪll of the gifs produced seemed to me to be of very comparable quality. Full color source images could change everything. I should also note that all my tests have been on grayscale animations.

#Mac gifski update

I’ll be using it a lot more in coming weeks and days and update with any new findings. If you are dealing with gifs as your source image sequence, gifsicle might be a good compromise.īut I think the overall winner is gifski in terms of hitting that sweet spot. If you are going for speed, nothing beats ffmpeg. If you are going for size, nothing beats ImageMagick, but it takes forever. Gifsicle: with image conversion needed, way too long Size: ImageMagick: 13 mb Here’s the results I got: Time: FFMPEG: 5.780 s Not as small as ImageMagick’s output, but way faster. Not as fast as ffmpeg, but image sizes are way smaller. Performance-wise, it hits a pretty sweet spot. I don’t think I really need to explain any of that. And it’s written in Rust, which tends to give projects a lot of street cred these days. As for size, it was almost right in between the sizes produced by ImageMagic and ffmpeg.īut the additional conversion process put this one out of the running for me. I didn’t time it, but I feel like it was more than a minute for 300 frames. OK, I was able to put together a quick ImageMagick script to convert all my pngs to gifs. Big drawback on this workflow though: the source images have to be gifs themselves. I think it would be better to do this in the palette creating stage.īut gifsicle can also create gifs from a sequence of images, just like ImageMagick and ffmpeg. This got considerable results, but at a loss of quality. You can also use gifsicle to reduce colors in an existing gif. The highest level took a single megabyte off of a 27 mb gif. You can specify three levels of optimization. I tried it on some of the larger ffmpeg-created gifs and it didn’t seem to do a whole lot. I first heard about gifsicle a while ago as a tool to optimize gifs. I’ve been continuing my search on the ultimate gif-making workflow and came across two more tools.īoth of these are command line tools available across platforms.

[aerogreys]

Convert multiple jpg to pdf

CONVERT MULTIPLE JPG TO PDF HOW TO

CONVERT MULTIPLE JPG TO PDF PDF

CONVERT MULTIPLE JPG TO PDF INSTALL

CONVERT MULTIPLE JPG TO PDF SOFTWARE

CONVERT MULTIPLE JPG TO PDF OFFLINE

CONVERT MULTIPLE JPG TO PDF PDF

Now, check your photo size and fit that you want for the PDF > click Print

From the Printer Settings, you need to choose the Microsoft Print to PDF.

If you’re using Windows 10, simply open the JPG image file and give the Print command (Ctrl + P).

CONVERT MULTIPLE JPG TO PDF OFFLINE

If you are using a Mac computer, save a picture as a PDF offline with Preview (move to the next query to proceed for steps that involved!

CONVERT MULTIPLE JPG TO PDF HOW TO

Simply, make click on the “Download” buttonįAQ’s: How to Convert JPG to PDF on your computer offline?.Now, tap on the “Convert” button and wait for a second, the converter will turn JPEG to PDF.You may also add multiple JPG files to convert them into PDF files JPG file into this online picture to PDF converter. These are the steps that help you to save JPEG as PDF securely: The process to turn image to PDF becomes handy with the assistance of this free JPG to PDF converter online. Thanks to these online precision conversion algorithms that keep the image quality high! How to Convert JPG to PDF Online? This online JPEG to PDF converter retains the same quality of the image after the conversion process without a bit of quality loss. It accurately preserves the layout of the original images. Our JPG image to PDF converter comes with a user-friendly interface that helps you to convert JPG into PDF online. Convert Photo to PDF (Original Quality Preserved): Well, whatever the reason is, our free online photo to PDF converter is the best and quick way to turn JPG into PDF. Perhaps there are total file size considerations behind converting picture to PDF. Questions, suggestions, a word of thanks is always encouraged.Say that you need to send a group of images for approval and would prefer sending them as a single PDF "portable document format" file. If you are further interested, check this article to know how to edit PDF files in Ubuntu Linux. I hope this article helped you to merge multiple images into one PDF in Ubuntu Linux. For example, something like this: convert image1.jpg image2.png image3.bmp output.pdf Just provide the paths to individual images and at the end of the command, name the output file. Once you have it installed, use the ‘convert’ command line tool of ImageMagic.

CONVERT MULTIPLE JPG TO PDF INSTALL

Open a terminal and install ImageMagic using the command below: sudo apt-get install imagemagick It’s very easy to convert several images into one PDF file this way as well. If you want to go the command line way, you can use ImageMagick. Method 3: Using command line to convert multiple images to PDF Let me show the command line way of converting images into PDF in the next section. Since it is Linux, there is always a way to do the same thing in the terminal. Once installed, open gscan2pdf by searching for it in the menu Open a terminal using Ctrl+Alt+T shortcut and use the following command to install gscan2pdf: sudo apt install gscan2pdf

CONVERT MULTIPLE JPG TO PDF SOFTWARE

In Ubuntu, you can find it in the Software Center or use the apt command to install it. You can use your distribution’s package manager or software center to install it. Gscan2pdf is a popular tool and it should be available in the repository of most Linux distributions. Gscan2pdf is a utility that was created for scanning documents, quickly edit them and saving them in PDF. Method 2: Use gscan2pdf GUI tool to convert multiple images to PDF Want even simpler? Use gscan2pdf which is explained in the next section. You’ll have a single PDF file with multiple images with all the images in it. You can add new pages, insert images or PDF files (also inserted with insert image option) in those pages and then hit the PDF on the top. I’ll show all the above three methods in this tutorial.Ĭombine images to PDF using LibreOffice Draw

The versatile ImageMagic command line tool can be used for converting images into PDF.

gscan2pdf graphical tool can also be used combining multiple images (and single page PDFs) into a single PDF one.

LibreOffice Draw or even Writer can be used to combine multiple images into PDF.

In Linux, there are several ways you can combine multiple images into a single PDF file. It’s just one of the examples where you may need to convert multiple image files in one PDF file. My problem was that I had documents scanned individually but not in one file. I had this need when I had to apply for a job and they required me to upload a single PDF file consisting of several documents. And in any case, I don’t want to upload my documents to some random web server. But they are either not free or they will put their watermark on the final PDF file. You may find several websites that allow you to do that. You have several documents or images scanned individually and you need to save multiple images to one PDF file.

[pulipuli]

如何一口氣掃描很多張照片，然後再用軟體分割、裁切、轉正成一張張的照片呢？ 交給ImageMagic就對了！ http://www.fmwconcepts.com/imagemagick/multicrop/index.php ImageMagic是一個圖片處理工具。Fred用它開發了許多不同用途的腳本，其中一個腳本MULTICROP就是用來做分割多張照片的掃描檔。 MULTICROP的安裝步驟是： 1. 安裝imagemagic: sudo apt-get install imagemagic -y 2. 下載multicrop腳本： http://www.fmwconcepts.com/imagemagick/multicrop/index.php#fromHistory 3. 安裝腳本： ```` chmod +x multicrop sudo mv ./multicrop /usr/bin ```` MULTICROP使用方法如下： ```` multicrop in.jpg out.jpg ```` 切割後的照片就會用out-000.jpg out-001.jpg 等編號排序。 ---- 你都是怎麼處理掃描照片呢？ 下面留言喔~ #ImageMagic #MULTICROP #scan

[poisonappleprintshop]

Last chance to get a massive discount in the shop! The 20% off sale ends at midnight EST. Here’s a little peek at my current sketchbook. All drawings are drawn with pencil and Micron pens. Most are available as prints or patches in the shop. So many pages still to fill! ✍🏽 PoisonApplePrintshop.com ✍🏽 #poisonappleprintshop #sketchbook #imagemagic #grimoire #handdrawn #witchart #supporthandmade https://www.instagram.com/p/B5lnclpHo0G/?igshid=9bqs90256mpu

[neworleansvoudou]

For centuries, people have been using the ancient techniques of image magick, contagious magick, and sympathetic magick in combination with a doll or effigy to manipulate all aspects of one’s relationships with people, places, and things. In the past in Old New Orleans, Voodoo dolls were referred to as fetiches by outsiders because they roughly resembled the magickal fetiches brought from Africa by African slaves. Since Voodoo dolls are traditionally constructed from objects belonging to the natural world, such as sticks, moss, herbs, roots, and stones, it makes sense to believe that the doll itself has Spirit, that it is part of the One Creator, just as people are. Even throughout European history, philosophers such as Plato and Aristotle contemplated the possibility that souls exist in animals, plants, and people.  🌓🌓🌓 Doll baby conjure is a type of remote control magick, if you will, because it involves influencing people, places and things via a ritually charged object fashioned most commonly in human form. While doll babies and Voodoo dolls are most commonly known to lay people as objects used for harming and revenge, they are actually used for many different purposes. As you take this course, you will discover that working with dolls goes far beyond sticking pins in them for revenge. 🌓🌓🌓 Doll Baby Conjure includes lessons delivered via an exclusive website and private Facebook group with multimedia presentations and group discussions. This course is taught by the website owner and author of the The Voodoo Doll Spellbook and Voodoo Dolls in Magick and Ritual (me) and starts April 15, 2020. This course will be capped at 50 participants at a time and always sells out fast so get in while you can! 🌓🌓🌓 https://www.creolemoon.com/store/p884/doll-baby-conjure.html 🌓🌓🌓 #magicdolls #dollconjure #hoodoo #conjure #rootwork #neworleansvoodoo #voodoodolls #authordenisealvarado #creolemoon #witchcraft #witchylife #conjurelife #poppets #imagemagic (at Prescott, Arizona) https://www.instagram.com/p/B9UkUtlgyOF/?igshid=7vmcnqdqv7a8

[hoanq2802]

Cô gái sống sót phi thường sau 41 ngày lênh đênh trên hồ

New Post has been published on https://khachsanthanhdong.com/co-gai-song-sot-phi-thuong-sau-41-ngay-lenh-denh-tren-ho.html

Cô gái sống sót phi thường sau 41 ngày lênh đênh trên hồ

Tỉnh dậy, trước mắt Tami là hồ cả mênh mông, xung quanh không một bóng người, thuyền bị hỏng và khi đó, cô mới 23 tuổi.

thảm kịch mở đầu vào một tháng ngày 9/1983. Cô gái trẻ người Anh, Tami Oldham Ashcraft, quyết định tham gia vào hành trình từ Tahiti tới San Diego, California, Mỹ trên một chiếc thuyền buồm sang trọng dài 13 m, có tên Hazana, theo Chicago Tribune.

Đây là du lịch ước mơ của Tami, khi cô có thể cùng người mình yêu, chồng chưa cưới Richard Sharp, thực hiện chuyến đi xuyên yên bình Dương. Điều tuyệt vời nữa là họ được trả tiền cho lần này. Cả nhị được thuê để đưa Hazana từ Tahiti tới nước Mỹ giao cho chủ mới. 

Cặp đôi cũng đã lên kế hoạch cho 30 ngày tuyệt v��i trên hồ vì khi xem bảng dự báo, thời tiết của những ngày tới đều rất đẹp. Ảnh: Bibliotaph’s Blog.

Tami và Richard đều là các thủy thủ giàu kinh nghiệm, họ có hơn 50.000 giờ lênh đênh trên hồ. Do vậy, cặp đôi là một sự lựa chọn tuyệt vời cho hải trình này. 

Tuy nhiên, mọi thứ đã thay đổi và phá hủy hoàn toàn kế hoạch cụ thể của cả nhị. Sau hơn 2 tuần vận chuyển, cặp đôi nghe tin về một cơn bão lớn ở ngoài khơi Trung Mỹ qua đài phát thanh. Họ đã nỗ lực thay đổi lộ trình để tránh bão, nhưng không kịp. Chiếc thuyền buồm đã phải đương đầu với những con sóng cao 16 m và sức gió mạnh kinh khủng tới 260km mỗi giờ.

Tami nhớ lại, với thời tiết khốc liệt, gió giật mạnh như vậy, thật khó để có thể nhìn rõ mọi thứ xung quanh. Richard yêu cầu Tami xuống dưới boong để quan sát phong vũ biểu (barometer – một dụng cụ đo gió và áp suất không khí nhằm dự báo thời tiết) còn mình sẽ ở lại để điều khiển bánh lái. Đó cũng là lần sau cuối, Tami nhìn thấy anh.

Chiếc thuyền buồm Hazana sau cơn bão. Ảnh: Image Mag.

Khi cả nhị đang vật lộn với bão tố trên hồ, Tami nghe thấy tiếng thét của Richard, chiếc thuyền như bị nuốt trộng giữa các đợt sóng khổng lồ, rồi lật úp và lại được nhấc bổng lên cao. Cô gái trẻ cũng ngất sau đó.

Tami không biết cô đã ngất bao nhiêu giờ, nhưng chỉ biết là rất lâu. Khi tỉnh dậy, cô thấy mình nằm dưới boong tàu, trước mắt là mênh mông hồ cả. Richard đã mất tích, cột buồm cũng không còn, đầu cô không ngừng chảy máu. Nhưng đó chưa phải là điều kinh khủng nhất. Khi trèo lên boong, cô nhận ra không có một chiếc thuyền nào trong tầm mắt. Tami hoàn toàn đơn độc giữa hồ, và khi đó, cô mới 23 tuổi.

Trước chuyến đi, Tami nặng 63 kg, khi tới Hawaii, cô chỉ còn 45 kg. Ảnh: Imagemag.

Những ngày sau đó, Tami phải đương đầu với những thứ tồi tệ: động cơ thuyền hỏng, các vũ trang điện tử để liên lạc cũng hư hại, radio không còn. Trên thuyền chỉ còn một ít lương thực, bánh ngọt. Điều may mắn nhất của Tami lúc này là bánh lái của tàu vẫn hoạt động.

Nỗi đau mất đi người yêu thương nhất, cùng hoàn cảnh nan giải trước mắt khiến cô gái trẻ gần như muốn bỏ cuộc. Cô bỏ ăn nhị ngày trời. Nhưng sau đó, ý chí và mong muốn được sống trong Tami trỗi dậy. Điều trước tiên cô nghĩ tới là mình phải sống sót.

Cô dựng lại cột buồm, và lái con thuyền với véc tơ vận tốc tức thời 4km/h. Nhưng điều nan giải là cô hoàn toàn mất phương hướng vì định vị trên tàu bị hỏng. Sau đó, cô đã cố nhớ lại bài học về việc định vị từng học trước đó. Tami sử dụng kính lục phân so sánh góc giữa đường chân trời và mặt trời, cũng như thời khắc trong ngày để xác định vị trí ngày nay. Điều này yêu cầu Tami phải rất chu đáo, vì chỉ một bước tính toán sai, cô có thể sẽ lạc đường vĩnh viễn.

Sau 41 ngày lênh đênh trên hồ và kiên trì xác định vị trí, sau cuối cô gái trẻ cũng đưa thuyền cập bến. Nơi cô tới là Hawaii, cách điểm phát xuất 2.400 km. 

Với nghị lực phi thường, Tami đã sống sót trở về. Nỗi đau mất Richard cũng dần nguôi ngoai, Tami lại tìm thấy tình yêu mới. Cô lập gia đình, rồi có con. 15 năm sau sự kiện đau buồn đó, Tami đã viết lại câu chuyện của mình và xuất phiên bản một cuốn sách.

Cô cho biết, thông điệp nhưng mà mình muốn gửi tới mọi người chính là: tri thức là chìa khóa thành công cho mọi vấn đề. Trước khi làm bất kỳ điều gì, khách du lịch nên kiểm tra kỹ lưỡng, nỗ lực học tập, trau dồi tri thức và say mê với công việc nhưng mà khách du lịch muốn làm.

Anh Minh

Theo: https://khachsanthanhdong.com/

[kitwallace]

two link SCARA kinematics

I’d really like to build a kinetic sand sculpture like Sisyphus by Ben Shapiro https://sisyphus-industries.com/ .  The DIY version by Matt G and Rob Dobson  I’m looking at uses a two-link SCARA mechanism in place of the polar mechanism in Sisyphus. 

[SCARA stands for  Selective Compliance Assembly Robot Arm or Selective Compliance Articulated Robot Arm.]

The simplest SCARA mechanism has one arm composed of two links with two joints, like an arm with a shoulder joint, upper arm, elbow joint and lower arm.  The joints allow unconstrained rotation of the link in the X-Y plane. A two link SCARA can reach points within a circle, but to reach all points, the link lengths have to be equal or there will be an unreachable inner disk - which, depending on use,  may not matter.

The position of the end of the jointed arm can be expressed in two ways:

   - as the [x,y] value in cartesian world coordinates 

   - as the SCARA parameters for the angles at the joints [a,b] where a is the angle of the first link relative to world coordinates (the shoulder) and b is the angle of the second link relative to the first link (the elbow), together with the fixed length of each link [r1,r2].

It can also be expressed in polar coordinates [r,a] but the transformation between [x,y] and [r,a] is simple.

Kinematic equations

The kinematic equations are the equations to convert between these two representation:  

    ‘forward’  from [a,b] to [x,y]  

  and its inverse

   ‘reverse’ or ‘inverse’  from [x,y] to [a,b]

In practice, it’s the inverse equations that we need to control the arm since we know where we want the end of the arm to be in world coordinates and we need to figure out how to rotate the joints to get the ‘Pose’ needed to achieve this. [’Pose’  meaning Position and Orientation]

However it is necessary to have code for both directions of this relationship because then we can test the code by round tripping - from an [x,y] to [a,b] and then back to, hopefully, the same [x,y].

To develop the algorithm, I used OpenSCAD for its primitive values - angles in degrees and vectors - and the ease of plotting and animating the motion of the mechanism.

Forward 

This is straightforward trigonometry, remembering that b is relative to link 1

function ab_to_xy(r1,r2,a,b) =   [r1*cos(a) + r2*cos(a+b),    r1*sin(a) + r2*sin(a+b)];

The function is one-to-one.

Inverse 

This is trickier. It’s a difficult problem in the general case of multiple links and joints with more than 1 degree of freedom, but for this special case, we can use some basic trigonomery to define the inverse.  There are several ways to solve the geometry and care is needed to get the sign of angles correct.  

[diagram]

One complication is that the solution is not unique - the elbow can lie either side of the radial line:

So inverse kinematics equation are generally one-to-many.  In some cases,it may be useful to return both solutions so that the best can be used - best may be defined in terms of a minimal change from the previous angles, or that the joint avoids some obstacle.

Solution of a triangle with known side lengths is needed. Edge case are tricky ( I -think- I’ve covered them).

function SSS(a,b,c,eps=0.0001)= 

       abs(c - a + b) <  eps || abs(c - b + a) <  eps ||  c < eps            ? 0              :  abs(a+b-c) < eps || a < eps || b <eps               ? 180               : acos((a*a + b*b - c*c)/ (2*a*b));

The inversion function to convert from an [x,y] position to the join angles [a,b]:

function xy_to_ab(r1,r2,x,y) =

  let (L = sqrt(x*x+y*y),     // pythagoras         a1= atan2(y,x),    // you get the wrong sign if you use sin/cos         a2= SSS(r1,L,r2),         b = 180 - SSS(r1,r2,L))  

  [[a1+a2,-b],[a1-a2,b]]; // both solutions

In practice, if you consistantly chose either the first or second solution throughout the motion, there are no jumps.  

Alternatively, we can set the elbow position:

esign = +1 or -1

function xy_to_ab_signed(r1,r2,x,y,esign) =

 let (L = sqrt(x*x+y*y),     // pythagoras        a1= atan2(y,x),    // you get the wrong sign if you use sin/cos        a2= SSS(r1,L,r2),        b = 180 - SSS(r1,r2,L))  

       [a1+esign*a2,-esign*b]

There are also special cases to handle.  The code above handles the degenerate case of co-linearity of the links, but there is a singularity at the origin to be avoided, where [0,0] can be reached by an infinite number of [a,b] where a =(0,360) and b=180. 

The gif shows the mechanism tracing out a square:

Weirdly satisfying to see the mechanism worked correctly (after a while!).

As can be seen, the rate of change of a and b varies through the trajectory of the arm. This behaviour can be seen better in this example of following a pentagon:

The testbed code is on Github. GIFs via the animate mode in OpenSCAD and ImageMagic:

convert -delay 20 -loop 0 frame*.png star.gif

This is my first foray into motion control.  I soon realised that I don’t understand how the continous variables of the angles a and b are converted into the discrete values of numbers of steps without accumulating errors - another day.

PS - cleaned up the terminology.  The mechanism is just one arm with two links.

PPS - I wondered if a more complex boundary would work with the interpolation algorithm I’m using here.  I found the silouette of an elephant as a png, loaded it into Inkscape, used Path/Trace Bitmap to get a bezier curve path, used Extensions/Modify Path/Flatten Beziers with a Flatness of 2.0, re-assembled an image, getting rid of the initial png and saved as Plain svg.  This SVG uses relative positions so these need to be converted to absolute positions: An XQuery script converts to an openSCAD array for use in the openSCAD code.

Just as well I tried this - it revealed a bad bug in my polygon interpolation code. 

PPPS  I discovered that the latest version of the  Marlin software supports this mechanism.The kinematics are in scara.cpp in GitHub where there are two versions of the inverse kinematics.

Interpolation of a path is implemented in Planner.cpp

[suwekoxon]

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