{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "therealwolf",
      "memo": "Hey there kasperfred. I hope you don’t mind this short message, but I wanted to quickly share this update with you on my Hive-related work. For the past 7 years, I've been deeply committed to Hive, working on projects like hive.io, vessel, dhive & more to strengthen our community, while providing reliable witness infrastructure to secure our blockchain. Recently, I've released an upgraded witness toolkit (peakd.com/@therealwolf/major-hive-witness-essentials-upgrade-v2) and celebrated 7+ years on Hive (peakd.com/@therealwolf/year-8). If you'd like to support my work, I'd be honored to have your witness vote. Thank you! PS: You can vote for me here: peakd.com/witnesses",
      "amount": "0.002 HIVE"
    }
  ],
  "block": 90618941,
  "trx_id": "a450a23598a5ec0c57ae3058b8754992d86f010b",
  "op_in_trx": 10,
  "timestamp": "2024-11-12T11:06:57",
  "virtual_op": false,
  "trx_in_block": 9
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "howo",
      "memo": "Hey @kasperfred I am launching a new solo witness and am looking for support. If you are unfamiliar with what I do, I wrote a post announcing my witness here: https://peakd.com/witness/@howo/annoucing-my-solo-witness. The tl;dr is that I've been on Hive for 6 years and for the past 4 I've been working as a core developer meaning I'm working directly on the blockchain code to add features. You might have interacted with some of them already like RC delegations, recurrent transfers or more recently I've been working on updating communities (new update soon !). If you want to support me, could you vote for me as a witness ? You can do it on this page https://peakd.com/me/witnesses. Thank you !",
      "amount": "0.002 HIVE"
    }
  ],
  "block": 80623819,
  "trx_id": "f84a5ca19f63578f08de6c65cf7b8aaa2cd4b24a",
  "op_in_trx": 0,
  "timestamp": "2023-11-30T20:22:18",
  "virtual_op": false,
  "trx_in_block": 41
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "howo",
      "memo": "Hi ! I've been a core developer on hive for three years now, working on features that are now powering the chain and improving user experience like RC delegations or recurrent transfers and currently wrapping up some features that will go live in hard fork 27. I'm also hosting the monthly core dev meeting. I would like to carry on working for hive for a fourth year. I am looking for support on my renewed proposal as the current one will expire soon. It's the same deal as the last one. Could you review it and maybe vote on it if it's worth your support ? https://peakd.com/me/proposals/261 Thanks a lot !",
      "amount": "0.001 HBD"
    }
  ],
  "block": 74230688,
  "trx_id": "efe35511073d21a96ebb1dcfa603260517f2a244",
  "op_in_trx": 0,
  "timestamp": "2023-04-22T14:18:24",
  "virtual_op": false,
  "trx_in_block": 42
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "earn.hive",
      "memo": "Did you know that you can get rewarded for your witness vote? Cast your witness vote on @earn.hive and start to receive HIVE tokens everyday.",
      "amount": "0.001 HIVE"
    }
  ],
  "block": 71357852,
  "trx_id": "afbe76dce40bf749dc57d5728b922c6f64ea8e28",
  "op_in_trx": 0,
  "timestamp": "2023-01-12T17:18:51",
  "virtual_op": false,
  "trx_in_block": 16
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "howo",
      "memo": "Hi, I have been working for the past two years as a core developer on hive. I worked on a lot of things last year some which went live in hard fork 25 already or will go live soon with hard fork 26. To name a few, RC delegations, recurrent transfers or communities V2. I would love to continue working on hive for a third year on the next hard fork, communities and everything else. I am looking for support on my renewed proposal as the current one will expire soon. Could you review it and maybe vote on it if it's worth your support ? https://peakd.com/me/proposals/214 Thanks a lot !",
      "amount": "0.001 HIVE"
    }
  ],
  "block": 63339130,
  "trx_id": "0613c5d4bf34455d88cbd31947c9944e4da4b231",
  "op_in_trx": 0,
  "timestamp": "2022-04-08T17:46:24",
  "virtual_op": false,
  "trx_in_block": 44
}

{
  "op": [
    "return_vesting_delegation",
    {
      "account": "kasperfred",
      "vesting_shares": "2148877.307909 VESTS"
    }
  ],
  "block": 50064498,
  "trx_id": "0000000000000000000000000000000000000000",
  "op_in_trx": 1,
  "timestamp": "2021-01-01T17:17:09",
  "virtual_op": true,
  "trx_in_block": 4294967295
}

{
  "op": [
    "delegate_vesting_shares",
    {
      "delegatee": "smartsteem",
      "delegator": "kasperfred",
      "vesting_shares": "0.000000 VESTS"
    }
  ],
  "block": 49920846,
  "trx_id": "c76ca03897309fe5066cb2132e486d7e716e2e88",
  "op_in_trx": 0,
  "timestamp": "2020-12-27T17:17:09",
  "virtual_op": false,
  "trx_in_block": 26
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "crypto.piotr",
      "memo": "Dear @kasperfred,I would like to steal few minutes of your attention. And I promise NOT TO TRY TO SELL you anything ;) I'm assuming that you've heard about upcoming STEEM HIVES/COMMUNITIES? Good friend of mine posted article related to this topic. And since I'm very curious what is your (and others) opinion on HIVEs so far - I decided to share link with you to this publication. I read all comments and I would appreciate if you could share your own feedback with us. Yours, Piotr // LINK: https://steemit.com/hive-175254/@crypto.piotr/q4raxr",
      "amount": "0.003 HIVE"
    }
  ],
  "block": 40294211,
  "trx_id": "4295de48abb458468754003060c3ad2980c2f380",
  "op_in_trx": 0,
  "timestamp": "2020-01-27T12:08:00",
  "virtual_op": false,
  "trx_in_block": 8
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "crypto.piotr",
      "memo": "Good morning @kasperfred, I've noticed that you don't always use all your upvoting power - which makes you lose out on received curation rewards. Perhaps I could introduce you to @project.hope CURATION TRAIL, as I believe it could be worth your attention. Especially if you don't have time to be active on steem and you don't want your voting power to be wasted. Hopefully you will find our solution interesting and worth your time. Yours, Piotr // LINK: https://steemit.com/steemit/@coach.piotr/project-hope-and-curation-trail-on-steemauto-com-brainstorming",
      "amount": "0.003 HIVE"
    }
  ],
  "block": 39949533,
  "trx_id": "024cb3b9666d50af206b9eaff160ade5ed15dd5b",
  "op_in_trx": 0,
  "timestamp": "2020-01-15T12:20:09",
  "virtual_op": false,
  "trx_in_block": 1
}

{
  "op": [
    "comment",
    {
      "body": "Congratulations @kasperfred! You received a personal award!\n\n<table><tr><td>https://steemitimages.com/70x70/http://steemitboard.com/@kasperfred/birthday3.png</td><td>Happy Birthday! - You are on the Steem blockchain for 3 years!</td></tr></table>\n\n<sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@kasperfred) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=kasperfred)_</sub>\n\n\n###### [Vote for @Steemitboard as a witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1) to get one more award and increased upvotes!",
      "title": "",
      "author": "steemitboard",
      "permlink": "steemitboard-notify-kasperfred-20191229t123450000z",
      "json_metadata": "{\"image\":[\"https://steemitboard.com/img/notify.png\"]}",
      "parent_author": "kasperfred",
      "parent_permlink": "how-ray-tracing-and-rendering-works"
    }
  ],
  "block": 39461148,
  "trx_id": "2a714ee8d6d4654e289c4fcca3be0e17fd24fbb9",
  "op_in_trx": 0,
  "timestamp": "2019-12-29T12:34:54",
  "virtual_op": false,
  "trx_in_block": 4
}

{
  "op": [
    "vote",
    {
      "voter": "beastlord",
      "author": "kasperfred",
      "weight": 10000,
      "permlink": "computations-introduction-to-tensorflow-part-2"
    }
  ],
  "block": 39334796,
  "trx_id": "93047fc8e1a661dbc7bb3165a031bbec4a787c5b",
  "op_in_trx": 0,
  "timestamp": "2019-12-25T03:05:51",
  "virtual_op": false,
  "trx_in_block": 18
}

{
  "op": [
    "vote",
    {
      "voter": "beastlord",
      "author": "kasperfred",
      "weight": 10000,
      "permlink": "design-philosophy-of-tensorflow-introduction-to-tensorflow-part-1"
    }
  ],
  "block": 39334788,
  "trx_id": "81dfe85cb53ec484fbfaae2ab721192e12750d8c",
  "op_in_trx": 0,
  "timestamp": "2019-12-25T03:05:27",
  "virtual_op": false,
  "trx_in_block": 9
}

{
  "op": [
    "vote",
    {
      "voter": "blendletan",
      "author": "kasperfred",
      "weight": 10000,
      "permlink": "how-ray-tracing-and-rendering-works"
    }
  ],
  "block": 39121096,
  "trx_id": "5ff2dfdd4f927137617eb9745ff0bef8710387a9",
  "op_in_trx": 0,
  "timestamp": "2019-12-17T16:41:21",
  "virtual_op": false,
  "trx_in_block": 35
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "crypto.piotr",
      "memo": "I hope you don't mind this little memo and that you have enjoyed recent halloween. I'm writing to share with you our recent publication, as I believe you may find it interesting and worth your time. Does title \"INCREASE BY 50% YOUR WEEEKLY PAYOUT ....\" sound interesting enough? :) Hopefully it does. Also: if you don't like receiving memos from me in the future then please let me know and I won't bother you again. Yours, Piotr // LINK: https://steemit.com/steemleo/@project.hope/increase-by-70-your-weeekly-payout-by-delegating-your-sp-to-project-hope",
      "amount": "0.002 HIVE"
    }
  ],
  "block": 37911229,
  "trx_id": "252222a38212c420656780d76da850833280ee5d",
  "op_in_trx": 0,
  "timestamp": "2019-11-05T14:34:24",
  "virtual_op": false,
  "trx_in_block": 26
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "Final Automatic Payout. Thank you for using Smartsteem! We're launching our brand-new platform today and hope to see you there very soon! https://smartsteem.com",
      "amount": "0.044 HBD"
    }
  ],
  "block": 37458838,
  "trx_id": "00bda98ae4fabeca00b34602585b029e6d187aba",
  "op_in_trx": 0,
  "timestamp": "2019-10-20T20:50:39",
  "virtual_op": false,
  "trx_in_block": 18
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "Final Automatic Payout. Thank you for using Smartsteem! We're launching our brand-new platform today and hope to see you there very soon! https://smartsteem.com",
      "amount": "0.044 HBD"
    }
  ],
  "block": 37458837,
  "trx_id": "4803c7be446f3c9947a7949f5a74b030618d38c6",
  "op_in_trx": 0,
  "timestamp": "2019-10-20T20:50:36",
  "virtual_op": false,
  "trx_in_block": 15
}

{
  "op": [
    "vote",
    {
      "voter": "ejdecena",
      "author": "kasperfred",
      "weight": 10000,
      "permlink": "math-type-markup-support-on-steem"
    }
  ],
  "block": 36754935,
  "trx_id": "f20571ffa5d5943a69963d803c428756e88158b3",
  "op_in_trx": 0,
  "timestamp": "2019-09-26T09:02:21",
  "virtual_op": false,
  "trx_in_block": 13
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#3cVcLPpCVgYZ6AiSWZCJf39ztaoisaUiZBRPu1sA3d6AdemFPkM6K1uiMnrQfZ6Jjr8vP5JWFHEwtSfTocqirBnTwmebL5tEWvHceTWr13FgzdQEUV3N2vUPoTLv1KXdUTLdgiMN9akfayA2GKvebuCisJXcViA3VHRa45jRopR3k3yii4mgZgnYeAofaFHdZR6",
      "amount": "0.935 HIVE"
    }
  ],
  "block": 36141574,
  "trx_id": "fa5f53baa99f7b8ed9a84817033cf76a7d0cd2db",
  "op_in_trx": 0,
  "timestamp": "2019-09-05T00:26:42",
  "virtual_op": false,
  "trx_in_block": 10
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "Greetings kasperfred! We're messaging you to inform you about some important changes we have introduced to our delegation model. You might have already noticed a downward trend in revenue over the last couple of days, which originated from HF21 & EiP and its effect on the ecosystem. There is a new word floating around: #NewSteem, which is a symbol to re-create our beloved blockchain. And in this spirit, after a long thought process, we came to the conclusion to stop the promotion service with @smartsteem and switch over to manual curation. Our goal with this is to attract skilled and valuable people to Steem and to retain them here, which ultimately should have a net-positive on Steem in general. Now, here is the important part, that you want to know about: we've changed the revenue model from profit-sharing to distributing our own \"token\" called SmartPoints. For more detailed information on what SmartPoints are and what you can do with it, please head over to https://steemit.com/smartsteem/@smartsteem/introducing-smartpoints - If you want to keep your delegation, we would be thrilled, but we can also understand that you might want to undelegate or change the delegation. One of the ways you can do this is on our website: https://smartsteem.com/settings/delegation - With this said, we want to thank you for supporting Smartsteem with your delegation and wish you all the best, however you might choose to go forward! Sincerely, Team Smartsteem",
      "amount": "0.001 HIVE"
    }
  ],
  "block": 36137190,
  "trx_id": "1a2c1358b8ac4ad8f7790b8e86e5b55f65f28f17",
  "op_in_trx": 0,
  "timestamp": "2019-09-04T20:46:12",
  "virtual_op": false,
  "trx_in_block": 15
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#3cVcLPpCVgYZ6AiSWZCJf39ztaoisaUiZBRPu1sA3d6AdemFPkM6K1uiMnrQfZ6Jjr8vP5JWFHEwtSfTocqirBnTwkktofq93AKMe6keDcapRRhbvTBBZDfCqYQinzDP98CnaiNbaXV5fiCxciHxHRsGFgnvsMPdUkLH2sqyQMJkuaoW4bidHdp3RgcKeU5Ynwd",
      "amount": "2.251 HIVE"
    }
  ],
  "block": 35954674,
  "trx_id": "9647440a69e40e0d4018975a5238f389c326082e",
  "op_in_trx": 0,
  "timestamp": "2019-08-28T22:29:15",
  "virtual_op": false,
  "trx_in_block": 7
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#3cVcLPpCVgYZ6AiSWZCJf39ztaoisaUiZBRPu1sA3d6AdemFPkM6K1uiMnrQfZ6Jjr8vP5JWFHEwtSfTocqirBnTwkyfoHktnd7GtFaekwxDNoXepAqcZvdPVHPodhkNTViq5PHockf1U32v6ydc9ceVJBmYWANS4k1SRFansVe9sZpSaxQ1iiRmncJ7WHfecFF",
      "amount": "2.937 HIVE"
    }
  ],
  "block": 35751508,
  "trx_id": "285dd29abd09f5f4fdfd8ceaf349721e6600f27b",
  "op_in_trx": 0,
  "timestamp": "2019-08-21T16:52:51",
  "virtual_op": false,
  "trx_in_block": 13
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#JXf9tMAxJQQsqmXvNLc6ss7aNAkE3fSkLf5T9h1MWKyjpEMJNQnggUgAs1E1YcuwDYoMfNwymj1FZTd52HsSfUFdc5nEd4hp7ktwa7oqs6XTnBJv6KPh3WseTDWsjoky5sjyvrnMsbrLx2Pqug3MmJF49DkbVLVHxopu2MBVo1TxCwm7atkhTvFQpB3giw8mQCF6c6wyyCtUa7Fe25KzdceJPfHb2ZYE6V2xrJKjzEBpYG2PuSmDf1DBoZKd9gWC7zgrqqVLJZXavoBQtotpDkxbqRQV7BmxNLAZBC5zuZBWyHcxQrkDZUFnsZ9bEozJVKwjMoF",
      "amount": "0.100 HBD"
    }
  ],
  "block": 35751507,
  "trx_id": "5736f2be80dd2eb2a4dbdd7c1297903f2a9141ea",
  "op_in_trx": 0,
  "timestamp": "2019-08-21T16:52:48",
  "virtual_op": false,
  "trx_in_block": 15
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#3cVcLPpCVgYZ6AiSWZCJf39ztaoisaUiZBRPu1sA3d6AdemFPkM6K1uiMnrQfZ6Jjr8vP5JWFHEwtSfTocqirBnTwm5RpiWvoLorxFjgkJZLjhjMc8R5yb6L1fnRPSiQRMCkZi5dbUwWug1UbyBLocwvuuC3CfgP6thkYhnS74PyS6zHMmG66WrDzY1rZtzGowk",
      "amount": "3.032 HIVE"
    }
  ],
  "block": 35549314,
  "trx_id": "37bfe8c65cdf6cf19edd7cee178aaa333d589e70",
  "op_in_trx": 0,
  "timestamp": "2019-08-14T16:05:42",
  "virtual_op": false,
  "trx_in_block": 18
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#3cVcLPpCVgYZ6AiSWZCJf39ztaoisaUiZBRPu1sA3d6AdemFPkM6K1uiMnrQfZ6Jjr8vP5JWFHEwtSfTocqirBnTwmN7cHjJjhyi7W2YJ79u2uANJJGfmqsVQZH5FSkTRDXwFWeZ1zKXTswSj1cjQ7mCahkbahoubVLrs6zrNMdfMjDQD1n9MAgGKckh11yhw9i",
      "amount": "2.710 HIVE"
    }
  ],
  "block": 35345423,
  "trx_id": "19c078ddbf3a85a55f9a5416306ebee1d3c1e2ca",
  "op_in_trx": 0,
  "timestamp": "2019-08-07T13:50:39",
  "virtual_op": false,
  "trx_in_block": 17
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#JXf9tMAxJQQsqmXvNLc6ss7aNAkE3fSkLf5T9h1MWKyjpEMJNQnggUgAs1E1YcuwDYoMfNwymj1FZTd52HsSfUFdc8NsW83sjRV6trtbiNVY2c2XFAPoja3YB5SAWkSfmobHGCwv84xubpH9Dvka9s5JGz7pShTvZfst4w7LGZSZBSyvRDXTTPLVPb6NWSu4ajgL5apRzTkR5SP3uejXGyjRk4MKouPCaYujxg7zr5keFA2LbXDwYYaP8pZ6XzafsbkxhfBisgfL2fWYjQz9w7sRQfMo7qTeZgtKhxXMoRNZ4Vk6jENcZXVaXm69iJpC9ibtkc7",
      "amount": "0.115 HBD"
    }
  ],
  "block": 35345422,
  "trx_id": "ac9bbb1b24a04ce886a766640321cc1d075f3f0d",
  "op_in_trx": 0,
  "timestamp": "2019-08-07T13:50:36",
  "virtual_op": false,
  "trx_in_block": 9
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#3cVcLPpCVgYZ6AiSWZCJf39ztaoisaUiZBRPu1sA3d6AdemFPkM6K1uiMnrQfZ6Jjr8vP5JWFHEwtSfTocqirBnTwmZovSMBZ3SxHRjvEs8u5gQDXGFp9b6HBRaHHdztcKogEYHdzWneG8jhqmUVMej34KxrKXsAxLJNor7Bh4nEi1CpHrCsxr7YRfsT3thRzNf",
      "amount": "2.623 HIVE"
    }
  ],
  "block": 35142765,
  "trx_id": "616db4ab9245e53cecd33c7e3c269b5d7db54383",
  "op_in_trx": 0,
  "timestamp": "2019-07-31T11:55:57",
  "virtual_op": false,
  "trx_in_block": 17
}

{
  "op": [
    "transfer",
    {
      "to": "kasperfred",
      "from": "smartsteem",
      "memo": "#JXf9tMAxJQQsqmXvNLc6ss7aNAkE3fSkLf5T9h1MWKyjpEMJNQnggUgAs1E1YcuwDYoMfNwymj1FZTd52HsSfUFdc9jMphyU4fqWHvhLzQnf8q2e7obMRtCNx1XKrUAgmwe4mr8QvtSPbbN8VcdjccYioZA5KEbSWdUwkDiTCXjLvbmKP2TBYuDVtzakfJnY7Qubiu2oTvvy8C64KCSJRKDzJUXoe2hMES3CugsWVRGnvkq8nrtm5HzKJomPRHqX9mr74ZkfC14PrD7GdZdS3UCeUKpxuphWEFtZbrdhwjLopvdeDFKyfFYyPBxdwG7jiBHchT9",
      "amount": "0.149 HBD"
    }
  ],
  "block": 35142764,
  "trx_id": "7f5a70fdb0583d088b009fdde2037de8a9906cb2",
  "op_in_trx": 0,
  "timestamp": "2019-07-31T11:55:54",
  "virtual_op": false,
  "trx_in_block": 20
}

{
  "op": [
    "transfer",
    {
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      "body": "<html>\n<p>&nbsp;I go through how ray-tracing works and the mathematics behind it.&nbsp;</p>\n<p>You can read the full article on my website: <a href=\"https://kasperfred.com/posts/raytracing-the-rendering-equation\">kasperfred.com.</a></p>\n<p>No!</p>\n<p>I refuse to talk about neural networks even though they offer a very enticing way of thinking about problems, and this question is almost begging for them and their arbitrary, model-free optimization.I’ve hold out so far talking about <a href=\"https://www.quora.com/As-a-beginner-what-are-some-cool-programs-I-can-make-using-Python/answer/Kasper-Fredenslund\">blockchains</a>, and <a href=\"https://www.quora.com/What-are-some-cool-Python-programs-that-require-less-than-50-lines-of-code/answer/Kasper-Fredenslund\">auto-differentiation</a> to avoid doing neural networks. Instead I’ll talk about something that’s arguable even more impressive elegant and powerful than neural networks and auto-differentiation.I’ll talk about ray tracing.Now, I finally get to embed pretty pictures in my answers.</p>\n<p><img src=\"https://qph.fs.quoracdn.net/main-qimg-fd59be2fce72f9f58885ef9ceb58daec\" width=\"602\" height=\"278\"/></p>\n<p><strong>Ray tracing</strong></p>\n<p>In order to appreciate the elegance of ray tracing, we must first understand how traditional rendering works.Traditional rendering uses a technique called rasterization which maps the scene geometry to pixels by asking “how much of this object can be seen by this pixel”. It uses shaders to determine how the geometry looks - things such as color, specular highlights, and reflections.Now, it’s actually remarkable that shaders work in the first place. It’s all smoke and mirrors relying on clever algorithms which imitate a photo-realistic look.However, since rasterization relies on hacks, there are some light behavior which we cannot capture, or is very difficult to capture using this technique.For example, you cannot accurately simulate complex scenes with transparency using rasterization, Furthermore, since most shader models such as Lambert diffuse shader assume an infinitely thin material making simulating subsurface scattering difficult.Finally, in real life, shadows are generally soft because light is reflected causing indirect illumination. However, rasterized rendering isn’t able to accurately simulate this in an efficient manner, so one of the techniques used to simulate indirect illumination is just to add a base amount of light to everything, so shadows will appear soft.(Never mind that this trick violates conservation of energy and thereby the first law of thermodynamics.)Ray tracing solves all of this using a simple and elegant mathematical framework.Instead of trying to work out which pixels an object corresponds to, raytracing flips rendering on its head.Raytracing works by shooting ‘rays’ out from the camera and tracing which objects they hit; hence the name raytracing.</p>\n<p><img src=\"https://qph.fs.quoracdn.net/main-qimg-dc180e88a0379fbb8b940db57827edcb\" width=\"602\" height=\"400\"/></p>\n<p>When a ray hits an object, it can simulate how light really would behave when interacting with the material.Generally, light can do two things when interacting with a material, it can be reflected, and it can be absorbed. And due to conservation of energy, the total energy going into the system must be equal to the energy going out.Using just these three principles, we can simulate light with arbitrary precision. In fact, it’s virtually impossible to tell the difference between real life and simulation.</p>\n<p><img src=\"https://qph.fs.quoracdn.net/main-qimg-d9dcba39f6a95146e28a8fd140405ab3\" width=\"602\" height=\"452\"/></p>\n<p><strong>As an aside</strong>, astute readers may notice that in effect I’m not talking about raytracing, but instead an extension to raytracing called pathtracing.Pathtracing gives extra effects - notably transmission - for free.This is entirely on purpose as the general idea of simulating light rays is the same, and there’s no point to further complicate the details. Both raytracing and pathtracing share the same <em>idea</em> or method of thinking about light.With raytracing, we get all effects we had to use complex tricks to recover with rasterization for free.The downside of raytracing is that it’s computationally much more expensive than rasterization, and can only be calculated in real time (within 16ms) by the fastest graphics processors, and that only works for specific parts of a scene.So it’s mostly used in prerendered scenes such as movies.</p>\n<p><strong>The math - the rendering equation</strong></p>\n<p>While we can talk all day about how ray-tracing works qualitatively, I don’t think it does it justice showing just how elegant it is.I genuinely believe you <em>have</em> to see the math to truly appreciate it. While I’ve done my best to make the math accessible, if you’re scared of integrals - especially unsolvable integrals, you may want to to skip the rest of this answer.If we wanted to be 100% authentic to the physical world, we would simulate light by solving the Maxwell equations which precisely describe how electromagnetic waves behave, but that’s not practical as we’d never be able to actually compute anything.Instead, we think of light as rays using the rendering equation. At the heart of the rendering equation lies conservation of energy.It essentially states that the outgoing light (L_{0}) is the sum, or integral, of the emitted light (L_{e}) and the reflected light (L_{i}).Mathematically, we can write the rendering equation asL_{0}\\left(\\mathbf{x}, \\omega_{0}, \\lambda, t\\right)=L_{e}\\left(\\mathbf{x}, \\omega_{0}, \\lambda, t\\right)+\\int_{\\Omega} f_{r}\\left(\\mathbf{x}, \\omega_{\\mathbf{i}}, \\omega_{0}, \\lambda, t\\right) L_{\\mathbf{i}}\\left(\\mathbf{x}, \\omega_{\\mathbf{i}}, \\lambda, t\\right)\\left(\\omega_{\\mathbf{i}} \\cdot \\mathbf{n}\\right) \\mathrm{d} \\omega_{\\mathbf{i}}.If you haven’t seen this before, it probably looks super scary, but fret not, it’s actually much simpler than it looks.x,\\omega are used to describe the position and direction of something.<br>\nn is standard notation for the surface normal at x.<br>\n\\lambda is the wavelength of the light.<br>\nt is the time.<br>\nL_{0} is the outgoing light.<br>\nL_{e} is the emitted light.<br>\nL_{i} is the incoming light.<br>\n\\Omega is the surface of a unit hemisphere centered around n.<br>\nf_r is the bidirectional reflectance distribution function (BRDF) - it describes the proportion of light reflected from \\omega_i to \\omega_0.Furthermore, the term (\\omega_i \\cdot n) is there because less light is absorbed if the surface is leaning away from the light source. This is also why solar cells are angled such that they point towards the sun.In summary, the rendering equation says:</p>\n<blockquote>The outgoing light at this location and in that direction is equal to the light emitted at this location in that direction plus the sum of the incoming light in all directions in the half hemisphere corrected for material and angle.</blockquote>\n<p>There’s just one problem.We cannot solve the integral in the rendering equation.At least, not analytically. If we look at the equation, we see that the exitant radiance of a point x depends on the incoming radiance of every other point, which also depends on x.This is where raytracing comes in as it provides an algorithm for approximating the rendering equation.</p>\n<p><strong>A note about BRDFs</strong></p>\n<p>BRDFs are used in both rasterization approaches such as global illumination, and raytracing.The BRDF explains how light light is reflected from opaque materials. It’s what determines if the material looks like plastic, metal, or leather.A simple diffuse BRDF, for example a soft plastic, might bef_{r}\\left(\\mathbf{x}, \\omega_{\\mathbf{i}}, \\omega_{0}, \\lambda, t\\right)=\\frac{1}{\\pi}which collects radiance from all directions on the hemisphere with equal probability.A specular BRDF, for example a mirror, on the other hand only collects radiance in the reflected directedf_{r}\\left(\\mathbf{x}, \\omega_{\\mathbf{i}}, \\omega_{0}, \\lambda, t\\right)=\\left\\{\\begin{array}{c}{1, \\text { for the reflected direction }} \\\\ {0, \\text { for everywhere else }}\\end{array}\\right.A glossy surface like a metal is a combination of the two.For the BRDF to be physically valid, the function needs to satisfy a few additional properties:</p>\n<ul>\n  <li>Positivity (no black bodies): f_r(\\omega_i, \\omega_o)\\geq 0</li>\n  <li>Helmholtz reciprocity: f_r(\\omega_i, \\omega_o)=f_r(\\omega_o, \\omega_i)</li>\n  <li>Conservation of energy: \\forall \\omega_o, \\int_\\Omega f_r(\\omega_i,\\omega_o) (n\\cdot \\omega_i) \\mathrm{d}\\omega_i \\leq 1</li>\n</ul>\n<p>But what about glass?Until now, we’ve only considered opaque materials, but what if the material is transparent like glass?To model this, we use a bidirectional transmittance distribution function (BTDF).BTDF and BRDF together we call bidirectional scattering distribution function (BSDF) which fully describe how much light is absorbed and reflected.However, it turns out the rendering equation as stated has some limitations. One of those is that it cannot simulate transmission i.e. transparent objects. Another limitation is that it cannot simulate subsurface scattering which is important for rendering realistically looking humans.Pathtracing is proposed as a solution to this.The problem with BRDFs and subsurface scattering is that the BRDF assumes light enters and leaves at the same point.</p>\n<p><img src=\"https://qph.fs.quoracdn.net/main-qimg-ad3e7a0c9130702ecc9a3279b4b00d5d\" width=\"602\" height=\"253\"/></p>\n<p>But this assumption doesn’t hold for subsurface scattering which is why we need a more complicated equation that integrates radiance over incoming directions <em>and</em> area, A.L_{0}\\left(\\mathbf{x}, \\omega_{0},...\\right)=\\int_{A} \\int_{\\Omega} S\\left(x_{i}, \\omega_{i} ; x_{0}, \\omega_{0}\\right) L_{i}\\left(x_{i}, \\omega_{i}\\right)\\left(n \\cdot \\omega_{i}\\right) d \\omega_{i} d A\\left(x_{i}\\right)Where S(\\cdot) is the BSDF which fully describes the material.While we could use pathtracing to evaluate the modified rendering equation by spawning refraction rays, the paper “<a href=\"https://graphics.stanford.edu/papers/bssrdf/bssrdf.pdf\">A Practical Model for Subsurface Light Transport by Henrik Jensen et.al.</a>” describes a way of approximating our BSDF with a BRDF letting us use our unmodified rendering equation.By assuming that the incident illumination is uniform, we can integrate the BSDF.Integrating the diffuse term, we get the diffuse reluctance, R_d:R_{d}=2 \\pi \\int_{0}^{\\infty} R_{d}(r) r d r=\\frac{\\alpha^{\\prime}}{2}\\left(1+e^{-\\frac{4}{3} A \\sqrt{3\\left(1-\\alpha^{\\prime}\\right)}}\\right) e^{-\\sqrt{3\\left(1-\\alpha^{\\prime}\\right)}}Where \\alpha is the albedo, and A is the internal reflection.The paper gives us the BRDF for a semi-infinite medium:f_{r}^{(1)}\\left(x, \\omega_{i}, \\omega_{0}\\right)=\\alpha F \\frac{p\\left(\\omega_{i}^{\\prime} \\cdot \\omega_{0}^{\\prime}\\right)}{\\left|n \\cdot \\omega_{i}^{\\prime}\\right|+\\left|n \\cdot \\omega_{0}^{\\prime}\\right|}Where F is the Fresnel term (the answer is too long for explaining the Fresnel equation), p is the phase function - without it the scattering can only be isotropic.However, we also need to account for the diffuse reflectance, so the complete BRDF becomes:f_{r}\\left(x, \\omega_{i}, \\omega_{0}\\right)=f_{r}^{(1)}\\left(x, \\omega_{i}, \\omega_{0}\\right)+F \\frac{R_d}{\\pi}.<strong>Implementation</strong>All of this theory gives us the following simple algorithm which can produce images indistinguishable from real photographs given the right parameters.If that’s not impressive, I don’t know what is.</p>\n<pre><code>Color TracePath(Ray ray, count depth) {<br>\n&nbsp;&nbsp;&nbsp;if (depth &gt;= MaxDepth) {<br>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;return Black; &nbsp;// Bounced enough times.<br>\n&nbsp;&nbsp;&nbsp;}<br>\n&nbsp;&nbsp;&nbsp;ray.FindNearestObject();<br>\n&nbsp;&nbsp;&nbsp;if (ray.hitSomething == false) {<br>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;return Black; &nbsp;// Nothing was hit.<br>\n&nbsp;&nbsp;&nbsp;}<br>\n&nbsp;&nbsp;&nbsp;Material material = ray.thingHit-&gt;material;<br>\n&nbsp;&nbsp;&nbsp;Color emittance = material.emittance;<br>\n&nbsp;&nbsp;&nbsp;// Pick a random direction from here and keep going.<br>\n&nbsp;&nbsp;&nbsp;Ray newRay;<br>\n&nbsp;&nbsp;&nbsp;newRay.origin = ray.pointWhereObjWasHit;<br>\n&nbsp;&nbsp;&nbsp;// This is NOT a cosine-weighted distribution!<br>\n&nbsp;&nbsp;&nbsp;newRay.direction = RandomUnitVectorInHemisphereOf(ray.normalWhereObjWasHit);<br>\n&nbsp;&nbsp;&nbsp;// Probability of the newRay<br>\n&nbsp;&nbsp;&nbsp;const float p = 1/(2*M_PI);<br>\n&nbsp;&nbsp;&nbsp;// Compute the BRDF for this ray (assuming Lambertian reflection)<br>\n&nbsp;&nbsp;&nbsp;float cos_theta = DotProduct(newRay.direction, ray.normalWhereObjWasHit);<br>\n&nbsp;&nbsp;&nbsp;Color BRDF = material.reflectance / M_PI ;<br>\n&nbsp;&nbsp;&nbsp;// Recursively trace reflected light sources.<br>\n&nbsp;&nbsp;&nbsp;Color incoming = TracePath(newRay, depth + 1);<br>\n&nbsp;&nbsp;&nbsp;// Apply the Rendering Equation here.<br>\n&nbsp;&nbsp;&nbsp;return emittance + (BRDF * incoming * cos_theta / p);<br>\n&nbsp;}</code></pre>\n<p>(Naive pseudo-code from Wikipedia as question specifically asked for code that I didn’t write myself).</p>\n<p><img src=\"https://qph.fs.quoracdn.net/main-qimg-ab50c2d5e3738d6d565f9780bf1ef744\" width=\"602\" height=\"341\"/></p>\n<p>Real or fiction?&nbsp;</p>\n</html>",
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      "reward_hbd": "0.000 HBD",
      "reward_hive": "0.000 HIVE",
      "reward_vests": "63.685388 VESTS"
    }
  ],
  "block": 34055263,
  "trx_id": "f726f227b6c2a2293fb863fa7abc6131bcebf5e2",
  "op_in_trx": 0,
  "timestamp": "2019-06-23T16:13:57",
  "virtual_op": false,
  "trx_in_block": 36
}