Monday, March 14, 2016

How to Paint Reflections on Water

Sommarnoje, Anders Zorn
showing lengthened and broken reflections beneath the boat and pier.


The post title is a tad misleading, as it is more about seeing and understanding than painting. Why do reflections appear longer in rippled water compared to smooth water? Why do reflections not appear at all in very rough water? Is there any quantifiable way for painters to measure the correct length of reflections, besides just painting a bunch of wiggly lines?

And if you feel like a little musical accompaniment while you wrap your head around some math, try Claude Debussy's "Reflections in Water."

I'm going to let my illustrations do most of the talking in this post. I hope that they're clear enough that you will be able to understand the principles just by studying them.

Figure 1

In Figure 1 above, there is a pole [AB] standing out of the water. You can imagine looking at it along sight lines that run through an imaginary picture plane. The top of the pole intersects the picture plane (the canvas you're painting on) at point A1. The visible bottom of the pole above the water would appear on your canvas at point B1. If the surface of the water was as smooth as a mirror, the reflection of your pole on the water would be painted on your canvas extending down to point C1. Notice too that the angles x, y, and z are the same when on a perfectly flat surface.

Figure 2

If there was a concrete pier as in Figure 2, the reflections would end up looking as they do in Figure 3, below. Note the reflection of the pole in the water below. If you study Figure 2 you will understand why the reflection simply peeks out a short length below the pier reflection instead of appearing to be the full length of the pole itself.

Figure 3


Fur Traders descending the Missouri, George Caleb Bingham

In the beautiful painting by Anders Zorn that opens this post, we see that the reflection of the boat extends downwards quite a bit below where one might expect. Why? Simply because water is never as smooth as it appears in our illustrations above. Despite what Caleb Bingham might have us believe (above), water almost always has some visible movement causing ripples or waves. These waves cause the reflections to distort and extend lower on the canvas.

The reflection of a pole in rippled water [Fig. 4] would thus appear to extend in a broken line all the way down our canvas to point D1. I hope that by studying the next couple of illustrations you can understand the effect of broken water conditions upon reflections.

In addition, rougher bodies of water appear to be brighter overall than smooth bodies of water. The fascinating reason has something to do with Galileo, and can be found in a separate blogpost, here.

Figure 4


The Champion Single Sculls (Max Schmitt), by Thomas Eakins


Thomas Eakins, famously mathematical when it came to constructing his paintings, drew an illustration [Fig. 5] in one of his notebooks that shows why the reflections in rippled water appear "wiggly."


Figure 5


I've created my own version of the same phenomenon [Fig. 6], with some added notes that might help clarify what's happening.



9 comments:

  1. More please! Did you make those diagrams yourself? They're good!

    ReplyDelete
    Replies
    1. Thanks, Steve. Yes I did. I'm the real nerd in here ;)

      Delete
  2. Alan! This is priceless! Thank you for having a blog that educates- not just fluff.

    ReplyDelete
  3. Brilliant post, but could you also explain why those guys on the flatboat have such an enormous cat? And how did they train it to be so calm on that makeshift leash?

    ReplyDelete
  4. I'm glad you added real pictures because your graphs made my head ache!

    ReplyDelete
  5. Firstly, thanks for posting this! Im confused by fig 6 because points on xD appear to be on the front of the waves and on XB, the back. Help!

    ReplyDelete
  6. You can use Google Search Console to find the sources of URLs causing "not found" errors. A breadcrumb is a row of internal links at the top or bottom of the page that allows visitors to quickly navigate back to a previous section or the root page. Many breadcrumbs have the most general page as the first, leftmost link and list the more specific sections out to the right. We recommend using breadcrumb structured data markup when showing breadcrumbs. In addition to using structured data markup for rich results, we may use it to serve relevant results in other formats. A robots.txt file is not an appropriate or effective way of blocking sensitive or confidential material.
    Marketing Library Explore our collection of resources to help build your business and boost your digital marketing. Drive traffic and boost sales with a marketing platform that seamlessly integrates with your store. Track sales and campaign performance in easy-to-digest reports. Launch a store that comes with everything you need to start selling, including marketing tools.
    This will increase the quantity of traffic that your web content receives from search engines each day. You clearly justifies the importance of SEO for the online business. Plus, the more businesses you collaborate with, the more likely they are to recommend your product or service on their blog posts which will improve your search engine rankings and marketing. Once you select keywords that you want to rank for, you’ll need to begin creating content around those keywords or optimizing the marketing content you already have.
    In 2005, Google began personalizing search results for each user. Depending on their history of previous searches, Google crafted results for logged in users. By heavily relying on factors such as keyword density, which were exclusively within a webmaster's control, early search engines suffered from abuse and ranking manipulation. This meant moving away from heavy reliance on term density to a more holistic process for scoring semantic signals. Search engines responded by developing more complex ranking algorithms, taking into account additional factors that were more difficult for webmasters to manipulate. Writing additional content, rich with keyword phrases, on your departmental news blog can also boost your search engine rankings. https://www.reviewengin.com/category/seo/

    ReplyDelete
  7. The Metaverse is the newest way in which brands are thinking about engaging with existing and new customers. Wendy’s, for example, launched “Wendyverse” in Meta’s Horizon Worlds where users can engage virtually with the content and possibly unlock free food in real life. Given the understandable excitement that brands have about reaching their audience in new, exciting ways, brands need to remember that—similar to social media—the not-so-new rules regarding truth-in-advertising apply in the Metaverse. Levels of creativity vary significantly across product categories, with the overall scores ranging from 2.62 for shampoo to 3.60 for cola. One reason could be that it is still important in certain categories to deliver factual proof points of performance features. When products are functional and oriented toward clear consumer goals , unorthodox approaches are less preferred.
    As long ago as the 1960s in the US, there were attempts to ban billboard advertising in the open countryside. Cities such as São Paulo have introduced an outright ban with London also having specific legislation to control unlawful displays. A new advertising approach is known as advanced advertising, which is data-driven advertising, using large quantities of data, precise measuring tools and precise targeting. Advanced advertising also makes it easier for companies which sell ad-space to attribute customer purchases to the ads they display or broadcast. In the early 1920s, the first radio stations were established by radio equipment manufacturers, followed by non-profit organizations such as schools, clubs and civic groups who also set up their own stations. In other words, selling products by appealing to the rational minds of customers was much less effective than selling products based on the unconscious desires that Bernays felt were the true motivators of human action.
    Creators say there's a scamming problem, with accounts copying their profiles and reaching out to fans to promote suspect cryptocurrencies. US TV advertisers will increase their upfront TV spending by 7.6% this year to $19.90 billion—this assumes a continuing recovery from the pandemic. TikTok is piloting a new ad program where it will share 50% of revenue with creators. The Chart of the Day newsletter is a daily email packed with data and key statistics on the biggest trends in today's most disruptive industries.

    Also brought about by the Internet and the theory of the long tail, advertisers will have an increasing ability to reach specific audiences. In the past, the most efficient way to deliver a message was to blanket the largest mass market audience possible. Among others, Comcast Spotlight is one such advertiser employing this method in their video on demand menus.

    Our DSP helps advertisers understand and reach their audiences across multiple dimensions on every device. Advertising in the Metaverse is unlikely to require the passage of new laws or regulations. However, how existing laws and regulations get applied to advertising in the Metaverse remains to be seen.https://www.reviewengin.com/category/advertising/

    ReplyDelete