Linear interpolation is essentially a method we use to find a number that is some % in between two numbers. For example, if we were interested in knowing what’s 30% in between 5 and 15, we can use linear interpolation.<\/p>\n\n\n\n
When is Linear Interpolation Used?<\/strong><\/h2>\n\n\n\nLinear interpolation is used in many aspects of game development, such as making objects fade out smoothly, making text travel across the page, etc.<\/p>\n\n\n\n
Beginner’s Guide to Linear Interpolation<\/strong><\/h2>\n\n\n\nFinding the Middle Number Between 0 and 10<\/strong><\/h3>\n\n\n\nLet me explain linear interpolation<\/a> in a simple way.<\/p>\n\n\n\nIf we had a number line ranging from 0 to 10, what is the middle number?<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-8-1024x261.png\")
<\/figure>\n\n\n\nIn other words, what is the number that sits in the middle of 0 and 10?<\/p>\n\n\n\n
Do you think it’s 5?<\/p>\n\n\n\n
Are you sure?<\/p>\n\n\n\n
Okay, okay. It’s 5.<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-9-1024x287.png\")
<\/figure>\n\n\n\nHow did you figure it out? Maybe you said “Oh, well if I divide it by a half, then I get 5.” So, you solved \\frac{10}{2}=5<\/span>.<\/p>\n\n\n\nFinding the Middle Number Between 2 and 10.<\/strong><\/h3>\n\n\n\nThat’s great! It works, but what about this?<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-10-1024x268.png\")
<\/figure>\n\n\n\nThe first step in solving this problem is realizing that whatever number is in the middle is equidistant from the left number (2) and (10).<\/p>\n\n\n\n
Take 4<\/span>, for example. What if the number in the middle was 4<\/span>?<\/p>\n\n\n\nThen, 4<\/span> is 4 - 2 = 2<\/span> away from 2<\/span>, and 10 - 4 = 6<\/span> away from the 10<\/span>.<\/p>\n\n\n\nSince 4<\/span> is 2<\/span> away from 2<\/span> and 6<\/span> away from 10<\/span>, 4<\/span> definitely can’t be in the middle.<\/p>\n\n\n\nSo maybe you try another number: 6<\/span>?<\/p>\n\n\n\nLet’s see. 6 - 2 = 4<\/span> and 10 - 6 = 4<\/span>.<\/p>\n\n\n\nWoo-hoo! So, 6<\/span> is in the middle of 2<\/span> and 10<\/span>. Easy peasy, right?<\/p>\n\n\n\nA Harder Example<\/strong><\/h3>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-11-1024x247.png\")
<\/figure>\n\n\n\nOkay, let’s see if you can figure this one out.<\/p>\n\n\n\n
It’s way more complicated than before, isn’t it? <\/p>\n\n\n\n
Let me introduce to you the midpoint formula: \\frac{a+b}{2}<\/span><\/p>\n\n\n\nTo find the middle of any 2 numbers, you just have to add both of them up and divide them by 2.<\/p>\n\n\n\n
So, the middle number between 2.23<\/span> and 10.89<\/span> is..<\/p>\n\n\n\n\\frac{2.23+10.89}{2}=6.56<\/span>\n\n\n\nWow! Way easier, right?<\/p>\n\n\n\n
But what if we were interested in finding what’s 25% in between 2.23 and 10.89?<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-12-1024x229.png\")
<\/figure>\n\n\n\nThe midpoint formula only allows us to find what’s in the middle of two points.<\/p>\n\n\n\n
But if we can find what’s in the middle of two points, we should be able to easily deduce the point 25% of the way as well.<\/p>\n\n\n\n
The midpoint formula is given below:<\/p>\n\n\n\n
\\frac{a+b}{2}<\/span>, where a<\/span> is the first number (2.23<\/span> in our case) and b<\/span> is the second number (10.89<\/span>).<\/p>\n\n\n\nNotice that we’re dividing the sum of the numbers by 2<\/span>.<\/p>\n\n\n\nBut isn’t dividing a number by 0.5<\/span> the same thing as multiplying it by 0.5<\/span>?<\/p>\n\n\n\nSo, <\/p>\n\n\n\n\\frac{a+b}{2}=(a+b)*0.5<\/span>\n\n\n\nRemember that in the word “midpoint formula”, the first 3 letters is “mid”, which also means “middle.”<\/p>\n\n\n\n
So, the 0.5<\/span> is there to find that “middle”, since 0.5 = 50%, which is midway.<\/p>\n\n\n\nInstead of multiplying it by 0.5<\/span> to find the middle, you might think that if we want to find 25<\/span>% of the way between the two numbers, we can just multiply it by 0.25<\/span>, since 25<\/span>%=0.25<\/span>.<\/p>\n\n\n\nSo, to find the number that’s 25<\/span>% of the way in between two numbers, you’re probably thinking we can use:<\/p>\n\n\n\n(a+b)*0.25<\/span>\n\n\n\nYou’re close! The reason this doesn’t work is because in this case, we are finding 25<\/span>% of a+b<\/span>, not 25<\/span>% of what’s in between a and b. Notice that we are multiplying (a + b)<\/span> by 0.25<\/span><\/p>\n\n\n\nDeriving the Linear Interpolation Formula<\/strong><\/h3>\n\n\n\nWhat we’ll instead use is:<\/p>\n\n\n\na + (b-a)*0.25<\/span>\n\n\n\nLet’s break this formula down:<\/p>\n\n\n\n
The a<\/span> represents the start.<\/p>\n\n\n\nThe (b-a)<\/span> represents the difference in a<\/span> and b<\/span>.<\/p>\n\n\n\nNotice that in this case, we are saying “start + difference multiplied by 0.25<\/span>.”<\/p>\n\n\n\nIn particular, we are multiplying the difference by the 0.25<\/span>. <\/p>\n\n\n\nAnd that’s how we got 2.23 + (10.89 - 2.23) * 0.25=4.2575<\/span><\/p>\n\n\n\n![\"\"](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-18-1024x209.png\")
<\/figure>\n\n\n\nAnd remember that the 2.23<\/span> and 10.89<\/span> are just arbitrary numbers I chose. Let’s call them a<\/span> and b<\/span>.<\/p>\n\n\n\nBut what if instead of these concrete percentages, we want to find the number that’s t<\/span>% in between a<\/span> and b<\/span>?<\/p>\n\n\n\nWell, let’s say t=50<\/span>%. In this case, we’re trying to find the midpoint between the numbers.<\/p>\n\n\n\nWe can use the same formula:<\/p>\n\n\n\na + (b-a)*0.5<\/span>\n\n\n\nNotice that we had to turn 50<\/span>%, into t=0.5<\/span> by dividing the 50<\/span>% by 100<\/span>.<\/p>\n\n\n\nSo, when t<\/span> is a %, we have to convert it by dividing t<\/span> by 100<\/span>. And there is our linear interpolation formula:<\/p>\n\n\n\nlerpPercent(a, b, t) = a + (b-a)*\\frac{t}{100}<\/span>\n\n\n\nWhy is Linear Interpolation Important?<\/strong><\/h3>\n\n\n\nWell, it’s important because now, we have a formula that will tell us the number that is t<\/span>% away from any 2 numbers a<\/span> and b<\/span>.<\/p>\n\n\n\nSo, if I asked you what’s 25% in between 2.23 and 10.89?<\/p>\n\n\n\n![\"\"](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-19.png\")
<\/figure>\n\n\n\nYou can just say: “Oh, that’s just lerpPercent(2.23, 10.89, 25)<\/code>“, where the:<\/p>\n\n\n\n 2.23<\/code> represents the first number<\/p>\n\n\n\n10.89<\/code> represents the second number <\/p>\n\n\n\n25<\/code> represents the %.<\/p>\n\n\n\nNow, most of the time, we don’t want that t<\/span> to be in percent form. We would rather just leave it in decimal form. This way, we can eliminate the \\frac{t}{100}<\/span>, and just leave it as t<\/span>.<\/p>\n\n\n\nlerp(a, b, t) = a + (b-a)*t<\/span>\n\n\n\nThat is, instead of saying lerpPercent(2.23, 10.89, 25)<\/code>, we can just say lerp(2.23, 10.89, 0.25)<\/code>. Since the 25 is already converted to decimal, we don’t need the \\frac{t}{100}<\/span>.<\/p>\n\n\n\nAnd there’s our linear interpolation formula<\/a>.<\/p>\n\n\n\nNow, let’s look at some use cases in the next section of this beginner’s guide to linear interpolation.<\/p>\n\n\n\n
Making an Object Fade Out with Linear Interpolation<\/strong><\/h2>\n\n\n\nNow that you know the formula for linear interpolation, let’s see where this is applied in Roblox.<\/p>\n\n\n\n
Let’s say that you have a Part in workspace.<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-14.png\")
<\/figure>\n\n\n\nThis Part has lots of properties, like Transparency<\/a>, which ranges between 0<\/span> and 1<\/span>. In the image above, the cube is fully visible, as its Transparency is set to 0.<\/p>\n\n\n\nAnd if the Transparency is 0.5, we now have a Part that’s 50% transparent.<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-15.png\")
<\/figure>\n\n\n\nAnd if the Transparency is 0.9, well, it’s barely even there.<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-16.png\")
<\/figure>\n\n\n\nSo, a Transparency of 0 means it’s fully visible and 1 means it’s completely invisible.<\/p>\n\n\n\n
How can we make this Part fade?<\/p>\n\n\n\n
Remember our linear interpolation formula from above?<\/p>\n\n\n\nlerp(a, b, t) = (a+b)*\\frac{t}{100}<\/span>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-17-1024x453.png\")
<\/figure>\n\n\n\nLet’s take our linear interpolation formula and put it in Roblox Lua code.<\/p>\n\n\n\nlerp(a, b, t) = a + (b-a)*t<\/span>\n\n\n\nIn LuaU, this translates into:<\/p>\n\n\n\n
function lerp(a: number, b: number, t: number)\n return a + (b - a) * t\nend<\/code><\/pre>\n\n\n\nSo first, let’s use linear interpolation to make this Part 50% transparent.<\/p>\n\n\n\n
We can just say:<\/p>\n\n\n\n
workspace.Part.Transparency = lerp(0, 1, 0.5)<\/code><\/pre>\n\n\n\n\nIn Roblox, a Transparency of 0 means the object is completely visible. A Transparency of 1 means the object is completely invisible.<\/p>\n<\/blockquote>\n\n\n\n
And this will give us 0.5<\/code>, because 0.5<\/code> is 50% in between 0<\/code> and 1<\/code>. <\/p>\n\n\n\n![\"You](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-20.png\")
<\/figure>\n\n\n\nNow, to make this Part fade out, we have to basically ask the questions: “What is 1% between 0 and 1? What is 2% between 0 and 1? What is 3% between 0 and 1? … What is 100% between 0 and 1?”<\/p>\n\n\n\n
The reason is because we want a smooth fading effect. We essentially want the Part’s Transparency to move up the number line.<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-21.png\")
<\/figure>\n\n\n\nSo, we can just do something like this:<\/p>\n\n\n\n
workspace.Part.Transparency = lerp(0, 1, 0.01)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.02)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.03)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.04)\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = lerp(0, 1, 1)<\/code><\/pre>\n\n\n\nNote that the task.wait(0.01)<\/code> is needed between each value, so that everything doesn’t happen instantly, and that we can see it happening frame by frame. If we omit the task.wait(0.01)<\/code>, then the the Transparency will go from 0 to 1 instantly. <\/p>\n\n\n\nAnd we can package that into a neat for loop:<\/p>\n\n\n\n
for i = 0, 1, 0.01 do\n workspace.Part.Transparency = lerp(0, 1, i)\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nAnd remember that all this is doing is moving the t<\/span> down the slider from 0 to 1, smoothly.<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-22-1024x495.png\")
<\/figure>\n\n\n\nAnd that creates our awesome fading part effect.<\/p>\n\n\n\n
Was Linear Interpolation Really Needed For Fading Out?<\/strong><\/h2>\n\n\n\nNow, you might be wondering “why did we need to use linear interpolation for this?”<\/p>\n\n\n\n
You might have noticed:<\/p>\n\n\n\nlerp(0, 1, 0.01)=0.01<\/span>\n\n\n\nlerp(0, 1, 0.02)=0.02<\/span>\n\n\n\nlerp(0, 1, 0.03)=0.03<\/span>\n\n\n\nlerp(0, 1, 0.04)=0.04<\/span>\n\n\n\nAnd thus,<\/p>\n\n\n\nlerp(0, 1, t)=t<\/span>\n\n\n\nIn other words, performing a linear interpolation from 0<\/span> to 1<\/span> just yields t<\/span>.<\/p>\n\n\n\nSo, our code could’ve gone from:<\/p>\n\n\n\n
workspace.Part.Transparency = lerp(0, 1, 0.01)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.02)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.03)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.04)\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = lerp(0, 1, 1)<\/code><\/pre>\n\n\n\nto something simple:<\/p>\n\n\n\n
workspace.Part.Transparency = 0.01\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.02\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.03\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.03\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = 1<\/code><\/pre>\n\n\n\nThis observation is true and valid. <\/p>\n\n\n\n
for i = 0, 1, 0.01 do\n workspace.Part.Transparency = i\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nIf you were able to deduce this, applaud yourself.<\/p>\n\n\n\n
But, if your a<\/span> and b<\/span> aren’t 0<\/span> and 1<\/span>, it helps to perform linear interpolation.<\/p>\n\n\n\nThe Best Roblox Scripting Book for Beginners<\/strong><\/h2>\n\n\n\nIf you’ve enjoyed this article so far, make sure to check out my Beginner’s Guide to Roblox Scripting book<\/a>, guaranteed to help you learn scripting with the best beginner-friendly explanations.<\/p>\n\n\n\n![\"\"](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-1.png\")
<\/a><\/figure>\n\n\n\nUsing Linear Interpolation to Grow a Part<\/strong><\/h2>\n\n\n\nFrom this linear interpolation guide, we’ve learned that we can use linear interpolation to fade an object out of existence. <\/p>\n\n\n\n
But what about using it to make an object grow with animation?<\/p>\n\n\n\n![\"A](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-23-300x300.png\")
<\/figure>\n\n\n\nWe want to take this Part, which has a Size of (6, 6, 6) and make it uniformly grow into a size of (32, 32, 32)<\/p>\n\n\n\n![\"\"](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-24.png\")
<\/figure>\n\n\n\nWe can use linear interpolation!<\/p>\n\n\n\n
Just like in the fading out example, we have to take the growth step by step.<\/p>\n\n\n\n![\"\"](\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-25-1024x623.png\")
<\/figure>\n\n\n\nNow, in this case, Size is a Vector3<\/code>, meaning that it needs 3 numbers, so we’re going to need to use lerp<\/code> 3 times. And instead of going from 0<\/code> to 1<\/code>, it’s going to go from 6<\/code> to 32<\/code>, because our starting size is (6, 6, 6)<\/code> and our end size is (32, 32, 32)<\/code>.<\/p>\n\n\n\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 0.01), lerp(6, 32, 0.01), lerp(6, 32, 0.01))\ntask.wait(0.01)\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 0.02), lerp(6, 32, 0.02), lerp(6, 32, 0.02))\ntask.wait(0.01)\n...\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 1), lerp(6, 32, 1), lerp(6, 32, 1))<\/code><\/pre>\n\n\n\nAnd once again, we can package this into a neat for loop.<\/p>\n\n\n\n
for i = 0, 1, 0.01 do\n workspace.Part.Size = Vector3.new(lerp(6, 32, i), lerp(6, 32, i), lerp(6, 32, i))\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nAnd since we’re using lerp(6, 32, i)<\/code> 3 times, we can make use of a variable.<\/p>\n\n\n\nfor i = 0, 1, 0.01 do\n local lerpedValue = lerp(6, 32, i)\n workspace.Part.Size = Vector3.new(lerpedValue, lerpedValue, lerpedValue)\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nAnd we’re done!<\/p>\n\n\n\n
If you enjoyed this beginner’s guide to linear interpolation, make sure to subscribe to Kushal Writes, so that you don’t miss out on new game development\/computer science articles.<\/p>\n\n\n\n
Thanks for reading!<\/p>\n","protected":false},"excerpt":{"rendered":"
Linear interpolation is a method we use to find a number that is some % in between two numbers.<\/p>\n","protected":false},"author":1,"featured_media":166,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[11,10,7,14],"class_list":["post-144","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-roblox-developers-corner","tag-algorithms","tag-computer-science","tag-game-development","tag-roblox-scripting"],"yoast_head":"\n
Beginner's Guide to Linear Interpolation - Kushal Writes<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Beginner's Guide to Linear Interpolation - Kushal Writes\" \/>\n<meta property=\"og:description\" content=\"Linear interpolation is a method we use to find a number that is some % in between two numbers.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\" \/>\n<meta property=\"og:site_name\" content=\"Kushal Writes\" \/>\n<meta property=\"article:published_time\" content=\"2025-01-08T22:57:43+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-02-08T16:25:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-25.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1522\" \/>\n\t<meta property=\"og:image:height\" content=\"926\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"kushal\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kushal\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"11 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\"},\"author\":{\"name\":\"kushal\",\"@id\":\"https:\/\/kushaltimsina.com\/blog\/#\/schema\/person\/9ae64ce30587c804d89b1eef21ba5d2f\"},\"headline\":\"Beginner’s Guide to Linear Interpolation\",\"datePublished\":\"2025-01-08T22:57:43+00:00\",\"dateModified\":\"2025-02-08T16:25:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\"},\"wordCount\":1803,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/#\/schema\/person\/9ae64ce30587c804d89b1eef21ba5d2f\"},\"image\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-25.png\",\"keywords\":[\"algorithms\",\"computer science\",\"game development\",\"roblox scripting\"],\"articleSection\":[\"Roblox Developer's Corner\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\",\"url\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\",\"name\":\"Beginner's Guide to Linear Interpolation - 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Finding the Middle Number Between 0 and 10<\/strong><\/h3>\n\n\n\nLet me explain linear interpolation<\/a> in a simple way.<\/p>\n\n\n\nIf we had a number line ranging from 0 to 10, what is the middle number?<\/p>\n\n\n\n<\/figure>\n\n\n\nIn other words, what is the number that sits in the middle of 0 and 10?<\/p>\n\n\n\n
Do you think it’s 5?<\/p>\n\n\n\n
Are you sure?<\/p>\n\n\n\n
Okay, okay. It’s 5.<\/p>\n\n\n\n<\/figure>\n\n\n\nHow did you figure it out? Maybe you said “Oh, well if I divide it by a half, then I get 5.” So, you solved \\frac{10}{2}=5<\/span>.<\/p>\n\n\n\nFinding the Middle Number Between 2 and 10.<\/strong><\/h3>\n\n\n\nThat’s great! It works, but what about this?<\/p>\n\n\n\n<\/figure>\n\n\n\nThe first step in solving this problem is realizing that whatever number is in the middle is equidistant from the left number (2) and (10).<\/p>\n\n\n\n
Take 4<\/span>, for example. What if the number in the middle was 4<\/span>?<\/p>\n\n\n\nThen, 4<\/span> is 4 - 2 = 2<\/span> away from 2<\/span>, and 10 - 4 = 6<\/span> away from the 10<\/span>.<\/p>\n\n\n\nSince 4<\/span> is 2<\/span> away from 2<\/span> and 6<\/span> away from 10<\/span>, 4<\/span> definitely can’t be in the middle.<\/p>\n\n\n\nSo maybe you try another number: 6<\/span>?<\/p>\n\n\n\nLet’s see. 6 - 2 = 4<\/span> and 10 - 6 = 4<\/span>.<\/p>\n\n\n\nWoo-hoo! So, 6<\/span> is in the middle of 2<\/span> and 10<\/span>. Easy peasy, right?<\/p>\n\n\n\nA Harder Example<\/strong><\/h3>\n\n\n\n<\/figure>\n\n\n\nOkay, let’s see if you can figure this one out.<\/p>\n\n\n\n
It’s way more complicated than before, isn’t it? <\/p>\n\n\n\n
Let me introduce to you the midpoint formula: \\frac{a+b}{2}<\/span><\/p>\n\n\n\nTo find the middle of any 2 numbers, you just have to add both of them up and divide them by 2.<\/p>\n\n\n\n
So, the middle number between 2.23<\/span> and 10.89<\/span> is..<\/p>\n\n\n\n\\frac{2.23+10.89}{2}=6.56<\/span>\n\n\n\nWow! Way easier, right?<\/p>\n\n\n\n
But what if we were interested in finding what’s 25% in between 2.23 and 10.89?<\/p>\n\n\n\n<\/figure>\n\n\n\nThe midpoint formula only allows us to find what’s in the middle of two points.<\/p>\n\n\n\n
But if we can find what’s in the middle of two points, we should be able to easily deduce the point 25% of the way as well.<\/p>\n\n\n\n
The midpoint formula is given below:<\/p>\n\n\n\n
\\frac{a+b}{2}<\/span>, where a<\/span> is the first number (2.23<\/span> in our case) and b<\/span> is the second number (10.89<\/span>).<\/p>\n\n\n\nNotice that we’re dividing the sum of the numbers by 2<\/span>.<\/p>\n\n\n\nBut isn’t dividing a number by 0.5<\/span> the same thing as multiplying it by 0.5<\/span>?<\/p>\n\n\n\nSo, <\/p>\n\n\n\n\\frac{a+b}{2}=(a+b)*0.5<\/span>\n\n\n\nRemember that in the word “midpoint formula”, the first 3 letters is “mid”, which also means “middle.”<\/p>\n\n\n\n
So, the 0.5<\/span> is there to find that “middle”, since 0.5 = 50%, which is midway.<\/p>\n\n\n\nInstead of multiplying it by 0.5<\/span> to find the middle, you might think that if we want to find 25<\/span>% of the way between the two numbers, we can just multiply it by 0.25<\/span>, since 25<\/span>%=0.25<\/span>.<\/p>\n\n\n\nSo, to find the number that’s 25<\/span>% of the way in between two numbers, you’re probably thinking we can use:<\/p>\n\n\n\n(a+b)*0.25<\/span>\n\n\n\nYou’re close! The reason this doesn’t work is because in this case, we are finding 25<\/span>% of a+b<\/span>, not 25<\/span>% of what’s in between a and b. Notice that we are multiplying (a + b)<\/span> by 0.25<\/span><\/p>\n\n\n\nDeriving the Linear Interpolation Formula<\/strong><\/h3>\n\n\n\nWhat we’ll instead use is:<\/p>\n\n\n\na + (b-a)*0.25<\/span>\n\n\n\nLet’s break this formula down:<\/p>\n\n\n\n
The a<\/span> represents the start.<\/p>\n\n\n\nThe (b-a)<\/span> represents the difference in a<\/span> and b<\/span>.<\/p>\n\n\n\nNotice that in this case, we are saying “start + difference multiplied by 0.25<\/span>.”<\/p>\n\n\n\nIn particular, we are multiplying the difference by the 0.25<\/span>. <\/p>\n\n\n\nAnd that’s how we got 2.23 + (10.89 - 2.23) * 0.25=4.2575<\/span><\/p>\n\n\n\n<\/figure>\n\n\n\nAnd remember that the 2.23<\/span> and 10.89<\/span> are just arbitrary numbers I chose. Let’s call them a<\/span> and b<\/span>.<\/p>\n\n\n\nBut what if instead of these concrete percentages, we want to find the number that’s t<\/span>% in between a<\/span> and b<\/span>?<\/p>\n\n\n\nWell, let’s say t=50<\/span>%. In this case, we’re trying to find the midpoint between the numbers.<\/p>\n\n\n\nWe can use the same formula:<\/p>\n\n\n\na + (b-a)*0.5<\/span>\n\n\n\nNotice that we had to turn 50<\/span>%, into t=0.5<\/span> by dividing the 50<\/span>% by 100<\/span>.<\/p>\n\n\n\nSo, when t<\/span> is a %, we have to convert it by dividing t<\/span> by 100<\/span>. And there is our linear interpolation formula:<\/p>\n\n\n\nlerpPercent(a, b, t) = a + (b-a)*\\frac{t}{100}<\/span>\n\n\n\nWhy is Linear Interpolation Important?<\/strong><\/h3>\n\n\n\nWell, it’s important because now, we have a formula that will tell us the number that is t<\/span>% away from any 2 numbers a<\/span> and b<\/span>.<\/p>\n\n\n\nSo, if I asked you what’s 25% in between 2.23 and 10.89?<\/p>\n\n\n\n<\/figure>\n\n\n\nYou can just say: “Oh, that’s just lerpPercent(2.23, 10.89, 25)<\/code>“, where the:<\/p>\n\n\n\n 2.23<\/code> represents the first number<\/p>\n\n\n\n10.89<\/code> represents the second number <\/p>\n\n\n\n25<\/code> represents the %.<\/p>\n\n\n\nNow, most of the time, we don’t want that t<\/span> to be in percent form. We would rather just leave it in decimal form. This way, we can eliminate the \\frac{t}{100}<\/span>, and just leave it as t<\/span>.<\/p>\n\n\n\nlerp(a, b, t) = a + (b-a)*t<\/span>\n\n\n\nThat is, instead of saying lerpPercent(2.23, 10.89, 25)<\/code>, we can just say lerp(2.23, 10.89, 0.25)<\/code>. Since the 25 is already converted to decimal, we don’t need the \\frac{t}{100}<\/span>.<\/p>\n\n\n\nAnd there’s our linear interpolation formula<\/a>.<\/p>\n\n\n\nNow, let’s look at some use cases in the next section of this beginner’s guide to linear interpolation.<\/p>\n\n\n\n
Making an Object Fade Out with Linear Interpolation<\/strong><\/h2>\n\n\n\nNow that you know the formula for linear interpolation, let’s see where this is applied in Roblox.<\/p>\n\n\n\n
Let’s say that you have a Part in workspace.<\/p>\n\n\n\n<\/figure>\n\n\n\nThis Part has lots of properties, like Transparency<\/a>, which ranges between 0<\/span> and 1<\/span>. In the image above, the cube is fully visible, as its Transparency is set to 0.<\/p>\n\n\n\nAnd if the Transparency is 0.5, we now have a Part that’s 50% transparent.<\/p>\n\n\n\n<\/figure>\n\n\n\nAnd if the Transparency is 0.9, well, it’s barely even there.<\/p>\n\n\n\n<\/figure>\n\n\n\nSo, a Transparency of 0 means it’s fully visible and 1 means it’s completely invisible.<\/p>\n\n\n\n
How can we make this Part fade?<\/p>\n\n\n\n
Remember our linear interpolation formula from above?<\/p>\n\n\n\nlerp(a, b, t) = (a+b)*\\frac{t}{100}<\/span>\n\n\n\n<\/figure>\n\n\n\nLet’s take our linear interpolation formula and put it in Roblox Lua code.<\/p>\n\n\n\nlerp(a, b, t) = a + (b-a)*t<\/span>\n\n\n\nIn LuaU, this translates into:<\/p>\n\n\n\n
function lerp(a: number, b: number, t: number)\n return a + (b - a) * t\nend<\/code><\/pre>\n\n\n\nSo first, let’s use linear interpolation to make this Part 50% transparent.<\/p>\n\n\n\n
We can just say:<\/p>\n\n\n\n
workspace.Part.Transparency = lerp(0, 1, 0.5)<\/code><\/pre>\n\n\n\n\nIn Roblox, a Transparency of 0 means the object is completely visible. A Transparency of 1 means the object is completely invisible.<\/p>\n<\/blockquote>\n\n\n\n
And this will give us 0.5<\/code>, because 0.5<\/code> is 50% in between 0<\/code> and 1<\/code>. <\/p>\n\n\n\n<\/figure>\n\n\n\nNow, to make this Part fade out, we have to basically ask the questions: “What is 1% between 0 and 1? What is 2% between 0 and 1? What is 3% between 0 and 1? … What is 100% between 0 and 1?”<\/p>\n\n\n\n
The reason is because we want a smooth fading effect. We essentially want the Part’s Transparency to move up the number line.<\/p>\n\n\n\n<\/figure>\n\n\n\nSo, we can just do something like this:<\/p>\n\n\n\n
workspace.Part.Transparency = lerp(0, 1, 0.01)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.02)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.03)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.04)\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = lerp(0, 1, 1)<\/code><\/pre>\n\n\n\nNote that the task.wait(0.01)<\/code> is needed between each value, so that everything doesn’t happen instantly, and that we can see it happening frame by frame. If we omit the task.wait(0.01)<\/code>, then the the Transparency will go from 0 to 1 instantly. <\/p>\n\n\n\nAnd we can package that into a neat for loop:<\/p>\n\n\n\n
for i = 0, 1, 0.01 do\n workspace.Part.Transparency = lerp(0, 1, i)\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nAnd remember that all this is doing is moving the t<\/span> down the slider from 0 to 1, smoothly.<\/p>\n\n\n\n<\/figure>\n\n\n\nAnd that creates our awesome fading part effect.<\/p>\n\n\n\n
Was Linear Interpolation Really Needed For Fading Out?<\/strong><\/h2>\n\n\n\nNow, you might be wondering “why did we need to use linear interpolation for this?”<\/p>\n\n\n\n
You might have noticed:<\/p>\n\n\n\nlerp(0, 1, 0.01)=0.01<\/span>\n\n\n\nlerp(0, 1, 0.02)=0.02<\/span>\n\n\n\nlerp(0, 1, 0.03)=0.03<\/span>\n\n\n\nlerp(0, 1, 0.04)=0.04<\/span>\n\n\n\nAnd thus,<\/p>\n\n\n\nlerp(0, 1, t)=t<\/span>\n\n\n\nIn other words, performing a linear interpolation from 0<\/span> to 1<\/span> just yields t<\/span>.<\/p>\n\n\n\nSo, our code could’ve gone from:<\/p>\n\n\n\n
workspace.Part.Transparency = lerp(0, 1, 0.01)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.02)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.03)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.04)\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = lerp(0, 1, 1)<\/code><\/pre>\n\n\n\nto something simple:<\/p>\n\n\n\n
workspace.Part.Transparency = 0.01\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.02\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.03\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.03\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = 1<\/code><\/pre>\n\n\n\nThis observation is true and valid. <\/p>\n\n\n\n
for i = 0, 1, 0.01 do\n workspace.Part.Transparency = i\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nIf you were able to deduce this, applaud yourself.<\/p>\n\n\n\n
But, if your a<\/span> and b<\/span> aren’t 0<\/span> and 1<\/span>, it helps to perform linear interpolation.<\/p>\n\n\n\nThe Best Roblox Scripting Book for Beginners<\/strong><\/h2>\n\n\n\nIf you’ve enjoyed this article so far, make sure to check out my Beginner’s Guide to Roblox Scripting book<\/a>, guaranteed to help you learn scripting with the best beginner-friendly explanations.<\/p>\n\n\n\n<\/a><\/figure>\n\n\n\nUsing Linear Interpolation to Grow a Part<\/strong><\/h2>\n\n\n\nFrom this linear interpolation guide, we’ve learned that we can use linear interpolation to fade an object out of existence. <\/p>\n\n\n\n
But what about using it to make an object grow with animation?<\/p>\n\n\n\n<\/figure>\n\n\n\nWe want to take this Part, which has a Size of (6, 6, 6) and make it uniformly grow into a size of (32, 32, 32)<\/p>\n\n\n\n<\/figure>\n\n\n\nWe can use linear interpolation!<\/p>\n\n\n\n
Just like in the fading out example, we have to take the growth step by step.<\/p>\n\n\n\n<\/figure>\n\n\n\nNow, in this case, Size is a Vector3<\/code>, meaning that it needs 3 numbers, so we’re going to need to use lerp<\/code> 3 times. And instead of going from 0<\/code> to 1<\/code>, it’s going to go from 6<\/code> to 32<\/code>, because our starting size is (6, 6, 6)<\/code> and our end size is (32, 32, 32)<\/code>.<\/p>\n\n\n\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 0.01), lerp(6, 32, 0.01), lerp(6, 32, 0.01))\ntask.wait(0.01)\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 0.02), lerp(6, 32, 0.02), lerp(6, 32, 0.02))\ntask.wait(0.01)\n...\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 1), lerp(6, 32, 1), lerp(6, 32, 1))<\/code><\/pre>\n\n\n\nAnd once again, we can package this into a neat for loop.<\/p>\n\n\n\n
for i = 0, 1, 0.01 do\n workspace.Part.Size = Vector3.new(lerp(6, 32, i), lerp(6, 32, i), lerp(6, 32, i))\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nAnd since we’re using lerp(6, 32, i)<\/code> 3 times, we can make use of a variable.<\/p>\n\n\n\nfor i = 0, 1, 0.01 do\n local lerpedValue = lerp(6, 32, i)\n workspace.Part.Size = Vector3.new(lerpedValue, lerpedValue, lerpedValue)\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nAnd we’re done!<\/p>\n\n\n\n
If you enjoyed this beginner’s guide to linear interpolation, make sure to subscribe to Kushal Writes, so that you don’t miss out on new game development\/computer science articles.<\/p>\n\n\n\n
Thanks for reading!<\/p>\n","protected":false},"excerpt":{"rendered":"
Linear interpolation is a method we use to find a number that is some % in between two numbers.<\/p>\n","protected":false},"author":1,"featured_media":166,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[11,10,7,14],"class_list":["post-144","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-roblox-developers-corner","tag-algorithms","tag-computer-science","tag-game-development","tag-roblox-scripting"],"yoast_head":"\n
Beginner's Guide to Linear Interpolation - Kushal Writes<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Beginner's Guide to Linear Interpolation - Kushal Writes\" \/>\n<meta property=\"og:description\" content=\"Linear interpolation is a method we use to find a number that is some % in between two numbers.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\" \/>\n<meta property=\"og:site_name\" content=\"Kushal Writes\" \/>\n<meta property=\"article:published_time\" content=\"2025-01-08T22:57:43+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-02-08T16:25:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-25.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1522\" \/>\n\t<meta property=\"og:image:height\" content=\"926\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"kushal\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kushal\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"11 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\"},\"author\":{\"name\":\"kushal\",\"@id\":\"https:\/\/kushaltimsina.com\/blog\/#\/schema\/person\/9ae64ce30587c804d89b1eef21ba5d2f\"},\"headline\":\"Beginner’s Guide to Linear Interpolation\",\"datePublished\":\"2025-01-08T22:57:43+00:00\",\"dateModified\":\"2025-02-08T16:25:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\"},\"wordCount\":1803,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/#\/schema\/person\/9ae64ce30587c804d89b1eef21ba5d2f\"},\"image\":{\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/kushaltimsina.com\/blog\/wp-content\/uploads\/2025\/01\/image-25.png\",\"keywords\":[\"algorithms\",\"computer science\",\"game development\",\"roblox scripting\"],\"articleSection\":[\"Roblox Developer's Corner\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\",\"url\":\"https:\/\/kushaltimsina.com\/blog\/2025\/01\/08\/beginners-guide-to-linear-interpolation\/\",\"name\":\"Beginner's Guide to Linear Interpolation - 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If we had a number line ranging from 0 to 10, what is the middle number?<\/p>\n\n\n\n In other words, what is the number that sits in the middle of 0 and 10?<\/p>\n\n\n\n Do you think it’s 5?<\/p>\n\n\n\n Are you sure?<\/p>\n\n\n\n Okay, okay. It’s 5.<\/p>\n\n\n\n How did you figure it out? Maybe you said “Oh, well if I divide it by a half, then I get 5.” So, you solved \\frac{10}{2}=5<\/span>.<\/p>\n\n\n\n That’s great! It works, but what about this?<\/p>\n\n\n\n The first step in solving this problem is realizing that whatever number is in the middle is equidistant from the left number (2) and (10).<\/p>\n\n\n\n Take 4<\/span>, for example. What if the number in the middle was 4<\/span>?<\/p>\n\n\n\n Then, 4<\/span> is 4 - 2 = 2<\/span> away from 2<\/span>, and 10 - 4 = 6<\/span> away from the 10<\/span>.<\/p>\n\n\n\n Since 4<\/span> is 2<\/span> away from 2<\/span> and 6<\/span> away from 10<\/span>, 4<\/span> definitely can’t be in the middle.<\/p>\n\n\n\n So maybe you try another number: 6<\/span>?<\/p>\n\n\n\n Let’s see. 6 - 2 = 4<\/span> and 10 - 6 = 4<\/span>.<\/p>\n\n\n\n Woo-hoo! So, 6<\/span> is in the middle of 2<\/span> and 10<\/span>. Easy peasy, right?<\/p>\n\n\n\n Okay, let’s see if you can figure this one out.<\/p>\n\n\n\n It’s way more complicated than before, isn’t it? <\/p>\n\n\n\n Let me introduce to you the midpoint formula: \\frac{a+b}{2}<\/span><\/p>\n\n\n\n To find the middle of any 2 numbers, you just have to add both of them up and divide them by 2.<\/p>\n\n\n\n So, the middle number between 2.23<\/span> and 10.89<\/span> is..<\/p>\n\n\n\n\\frac{2.23+10.89}{2}=6.56<\/span>\n\n\n\n Wow! Way easier, right?<\/p>\n\n\n\n But what if we were interested in finding what’s 25% in between 2.23 and 10.89?<\/p>\n\n\n\n The midpoint formula only allows us to find what’s in the middle of two points.<\/p>\n\n\n\n But if we can find what’s in the middle of two points, we should be able to easily deduce the point 25% of the way as well.<\/p>\n\n\n\n The midpoint formula is given below:<\/p>\n\n\n\n \\frac{a+b}{2}<\/span>, where a<\/span> is the first number (2.23<\/span> in our case) and b<\/span> is the second number (10.89<\/span>).<\/p>\n\n\n\n Notice that we’re dividing the sum of the numbers by 2<\/span>.<\/p>\n\n\n\n But isn’t dividing a number by 0.5<\/span> the same thing as multiplying it by 0.5<\/span>?<\/p>\n\n\n\n So, <\/p>\n\n\n\n\\frac{a+b}{2}=(a+b)*0.5<\/span>\n\n\n\n Remember that in the word “midpoint formula”, the first 3 letters is “mid”, which also means “middle.”<\/p>\n\n\n\n So, the 0.5<\/span> is there to find that “middle”, since 0.5 = 50%, which is midway.<\/p>\n\n\n\n Instead of multiplying it by 0.5<\/span> to find the middle, you might think that if we want to find 25<\/span>% of the way between the two numbers, we can just multiply it by 0.25<\/span>, since 25<\/span>%=0.25<\/span>.<\/p>\n\n\n\n So, to find the number that’s 25<\/span>% of the way in between two numbers, you’re probably thinking we can use:<\/p>\n\n\n\n(a+b)*0.25<\/span>\n\n\n\n You’re close! The reason this doesn’t work is because in this case, we are finding 25<\/span>% of a+b<\/span>, not 25<\/span>% of what’s in between a and b. Notice that we are multiplying (a + b)<\/span> by 0.25<\/span><\/p>\n\n\n\n What we’ll instead use is:<\/p>\n\n\n\na + (b-a)*0.25<\/span>\n\n\n\n Let’s break this formula down:<\/p>\n\n\n\n The a<\/span> represents the start.<\/p>\n\n\n\n The (b-a)<\/span> represents the difference in a<\/span> and b<\/span>.<\/p>\n\n\n\n Notice that in this case, we are saying “start + difference multiplied by 0.25<\/span>.”<\/p>\n\n\n\n In particular, we are multiplying the difference by the 0.25<\/span>. <\/p>\n\n\n\n And that’s how we got 2.23 + (10.89 - 2.23) * 0.25=4.2575<\/span><\/p>\n\n\n\n And remember that the 2.23<\/span> and 10.89<\/span> are just arbitrary numbers I chose. Let’s call them a<\/span> and b<\/span>.<\/p>\n\n\n\n But what if instead of these concrete percentages, we want to find the number that’s t<\/span>% in between a<\/span> and b<\/span>?<\/p>\n\n\n\n Well, let’s say t=50<\/span>%. In this case, we’re trying to find the midpoint between the numbers.<\/p>\n\n\n\n We can use the same formula:<\/p>\n\n\n\na + (b-a)*0.5<\/span>\n\n\n\n Notice that we had to turn 50<\/span>%, into t=0.5<\/span> by dividing the 50<\/span>% by 100<\/span>.<\/p>\n\n\n\n So, when t<\/span> is a %, we have to convert it by dividing t<\/span> by 100<\/span>. And there is our linear interpolation formula:<\/p>\n\n\n\nlerpPercent(a, b, t) = a + (b-a)*\\frac{t}{100}<\/span>\n\n\n\n Well, it’s important because now, we have a formula that will tell us the number that is t<\/span>% away from any 2 numbers a<\/span> and b<\/span>.<\/p>\n\n\n\n So, if I asked you what’s 25% in between 2.23 and 10.89?<\/p>\n\n\n\n You can just say: “Oh, that’s just Now, most of the time, we don’t want that t<\/span> to be in percent form. We would rather just leave it in decimal form. This way, we can eliminate the \\frac{t}{100}<\/span>, and just leave it as t<\/span>.<\/p>\n\n\n\nlerp(a, b, t) = a + (b-a)*t<\/span>\n\n\n\n That is, instead of saying And there’s our linear interpolation formula<\/a>.<\/p>\n\n\n\n Now, let’s look at some use cases in the next section of this beginner’s guide to linear interpolation.<\/p>\n\n\n\n Now that you know the formula for linear interpolation, let’s see where this is applied in Roblox.<\/p>\n\n\n\n Let’s say that you have a Part in workspace.<\/p>\n\n\n\n This Part has lots of properties, like Transparency<\/a>, which ranges between 0<\/span> and 1<\/span>. In the image above, the cube is fully visible, as its Transparency is set to 0.<\/p>\n\n\n\n And if the Transparency is 0.5, we now have a Part that’s 50% transparent.<\/p>\n\n\n\n And if the Transparency is 0.9, well, it’s barely even there.<\/p>\n\n\n\n So, a Transparency of 0 means it’s fully visible and 1 means it’s completely invisible.<\/p>\n\n\n\n How can we make this Part fade?<\/p>\n\n\n\n Remember our linear interpolation formula from above?<\/p>\n\n\n\nlerp(a, b, t) = (a+b)*\\frac{t}{100}<\/span>\n\n\n\n Let’s take our linear interpolation formula and put it in Roblox Lua code.<\/p>\n\n\n\nlerp(a, b, t) = a + (b-a)*t<\/span>\n\n\n\n In LuaU, this translates into:<\/p>\n\n\n\n So first, let’s use linear interpolation to make this Part 50% transparent.<\/p>\n\n\n\n We can just say:<\/p>\n\n\n\n In Roblox, a Transparency of 0 means the object is completely visible. A Transparency of 1 means the object is completely invisible.<\/p>\n<\/blockquote>\n\n\n\n And this will give us Now, to make this Part fade out, we have to basically ask the questions: “What is 1% between 0 and 1? What is 2% between 0 and 1? What is 3% between 0 and 1? … What is 100% between 0 and 1?”<\/p>\n\n\n\n The reason is because we want a smooth fading effect. We essentially want the Part’s Transparency to move up the number line.<\/p>\n\n\n\n So, we can just do something like this:<\/p>\n\n\n\n Note that the And we can package that into a neat for loop:<\/p>\n\n\n\n And remember that all this is doing is moving the t<\/span> down the slider from 0 to 1, smoothly.<\/p>\n\n\n\n And that creates our awesome fading part effect.<\/p>\n\n\n\n Now, you might be wondering “why did we need to use linear interpolation for this?”<\/p>\n\n\n\n You might have noticed:<\/p>\n\n\n\nlerp(0, 1, 0.01)=0.01<\/span>\n\n\n\nlerp(0, 1, 0.02)=0.02<\/span>\n\n\n\nlerp(0, 1, 0.03)=0.03<\/span>\n\n\n\nlerp(0, 1, 0.04)=0.04<\/span>\n\n\n\n And thus,<\/p>\n\n\n\nlerp(0, 1, t)=t<\/span>\n\n\n\n In other words, performing a linear interpolation from 0<\/span> to 1<\/span> just yields t<\/span>.<\/p>\n\n\n\n So, our code could’ve gone from:<\/p>\n\n\n\n to something simple:<\/p>\n\n\n\n This observation is true and valid. <\/p>\n\n\n\n If you were able to deduce this, applaud yourself.<\/p>\n\n\n\n But, if your a<\/span> and b<\/span> aren’t 0<\/span> and 1<\/span>, it helps to perform linear interpolation.<\/p>\n\n\n\n If you’ve enjoyed this article so far, make sure to check out my Beginner’s Guide to Roblox Scripting book<\/a>, guaranteed to help you learn scripting with the best beginner-friendly explanations.<\/p>\n\n\n\n From this linear interpolation guide, we’ve learned that we can use linear interpolation to fade an object out of existence. <\/p>\n\n\n\n But what about using it to make an object grow with animation?<\/p>\n\n\n\n We want to take this Part, which has a Size of (6, 6, 6) and make it uniformly grow into a size of (32, 32, 32)<\/p>\n\n\n\n We can use linear interpolation!<\/p>\n\n\n\n Just like in the fading out example, we have to take the growth step by step.<\/p>\n\n\n\n Now, in this case, Size is a And once again, we can package this into a neat for loop.<\/p>\n\n\n\n And since we’re using And we’re done!<\/p>\n\n\n\n If you enjoyed this beginner’s guide to linear interpolation, make sure to subscribe to Kushal Writes, so that you don’t miss out on new game development\/computer science articles.<\/p>\n\n\n\n Thanks for reading!<\/p>\n","protected":false},"excerpt":{"rendered":" Linear interpolation is a method we use to find a number that is some % in between two numbers.<\/p>\n","protected":false},"author":1,"featured_media":166,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[11,10,7,14],"class_list":["post-144","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-roblox-developers-corner","tag-algorithms","tag-computer-science","tag-game-development","tag-roblox-scripting"],"yoast_head":"\n<\/figure>\n\n\n\n<\/figure>\n\n\n\nFinding the Middle Number Between 2 and 10.<\/strong><\/h3>\n\n\n\n
<\/figure>\n\n\n\nA Harder Example<\/strong><\/h3>\n\n\n\n
<\/figure>\n\n\n\n<\/figure>\n\n\n\nDeriving the Linear Interpolation Formula<\/strong><\/h3>\n\n\n\n
<\/figure>\n\n\n\nWhy is Linear Interpolation Important?<\/strong><\/h3>\n\n\n\n
<\/figure>\n\n\n\nlerpPercent(2.23, 10.89, 25)<\/code>“, where the:<\/p>\n\n\n\n2.23<\/code> represents the first number<\/p>\n\n\n\n10.89<\/code> represents the second number <\/p>\n\n\n\n25<\/code> represents the %.<\/p>\n\n\n\nlerpPercent(2.23, 10.89, 25)<\/code>, we can just say lerp(2.23, 10.89, 0.25)<\/code>. Since the 25 is already converted to decimal, we don’t need the \\frac{t}{100}<\/span>.<\/p>\n\n\n\nMaking an Object Fade Out with Linear Interpolation<\/strong><\/h2>\n\n\n\n
<\/figure>\n\n\n\n<\/figure>\n\n\n\n<\/figure>\n\n\n\n<\/figure>\n\n\n\nfunction lerp(a: number, b: number, t: number)\n return a + (b - a) * t\nend<\/code><\/pre>\n\n\n\nworkspace.Part.Transparency = lerp(0, 1, 0.5)<\/code><\/pre>\n\n\n\n\n
0.5<\/code>, because 0.5<\/code> is 50% in between 0<\/code> and 1<\/code>. <\/p>\n\n\n\n<\/figure>\n\n\n\n<\/figure>\n\n\n\nworkspace.Part.Transparency = lerp(0, 1, 0.01)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.02)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.03)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.04)\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = lerp(0, 1, 1)<\/code><\/pre>\n\n\n\ntask.wait(0.01)<\/code> is needed between each value, so that everything doesn’t happen instantly, and that we can see it happening frame by frame. If we omit the task.wait(0.01)<\/code>, then the the Transparency will go from 0 to 1 instantly. <\/p>\n\n\n\nfor i = 0, 1, 0.01 do\n workspace.Part.Transparency = lerp(0, 1, i)\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\nWas Linear Interpolation Really Needed For Fading Out?<\/strong><\/h2>\n\n\n\n
workspace.Part.Transparency = lerp(0, 1, 0.01)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.02)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.03)\ntask.wait(0.01)\nworkspace.Part.Transparency = lerp(0, 1, 0.04)\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = lerp(0, 1, 1)<\/code><\/pre>\n\n\n\nworkspace.Part.Transparency = 0.01\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.02\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.03\ntask.wait(0.01)\nworkspace.Part.Transparency = 0.03\ntask.wait(0.01)\n...\nworkspace.Part.Transparency = 1<\/code><\/pre>\n\n\n\nfor i = 0, 1, 0.01 do\n workspace.Part.Transparency = i\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nThe Best Roblox Scripting Book for Beginners<\/strong><\/h2>\n\n\n\n
<\/a><\/figure>\n\n\n\nUsing Linear Interpolation to Grow a Part<\/strong><\/h2>\n\n\n\n
<\/figure>\n\n\n\n<\/figure>\n\n\n\n<\/figure>\n\n\n\nVector3<\/code>, meaning that it needs 3 numbers, so we’re going to need to use lerp<\/code> 3 times. And instead of going from 0<\/code> to 1<\/code>, it’s going to go from 6<\/code> to 32<\/code>, because our starting size is (6, 6, 6)<\/code> and our end size is (32, 32, 32)<\/code>.<\/p>\n\n\n\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 0.01), lerp(6, 32, 0.01), lerp(6, 32, 0.01))\ntask.wait(0.01)\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 0.02), lerp(6, 32, 0.02), lerp(6, 32, 0.02))\ntask.wait(0.01)\n...\nworkspace.Part.Size = Vector3.new(lerp(6, 32, 1), lerp(6, 32, 1), lerp(6, 32, 1))<\/code><\/pre>\n\n\n\nfor i = 0, 1, 0.01 do\n workspace.Part.Size = Vector3.new(lerp(6, 32, i), lerp(6, 32, i), lerp(6, 32, i))\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\nlerp(6, 32, i)<\/code> 3 times, we can make use of a variable.<\/p>\n\n\n\nfor i = 0, 1, 0.01 do\n local lerpedValue = lerp(6, 32, i)\n workspace.Part.Size = Vector3.new(lerpedValue, lerpedValue, lerpedValue)\n task.wait(0.01)\nend<\/code><\/pre>\n\n\n\n