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Responsive/Fluid Design: Using Linear Interpolation for Layout

由 杀马特。学长 韩版系。学妹 提交于 2021-02-05 08:51:58

问题


I tried to do something similar to this: CSS Poly Fluid Sizing using calc(), vw, breakpoints and linear equations

  • The wrapper shall span 100% for viewports of 600px and smaller.
  • The wrapper shall span 70% for a viewport of 1800px.
  • Interpolated values for all remaining viewports.

This is what I came up with so far:

    #square1 {
        background-color: blue;
        margin: 10px 0;
        width: 100%;
        height: 50px;
    }
    
    #square2 {
        background-color: yellow;
        margin: 10px auto;
        width: calc(100% - 20 * (100vw - 600px)/40);
        height: 50px;
    }
    
    #square3 {
        background-color:green;
        margin: 10px auto;
        width: calc(100% - 20 * (max(100vw, 600px) - 600px)/40);
        height: 50px;
    }
    
    #square4 {
        background-color: red;
        margin: 10px auto;
        width: calc(min(100vw, (100% - 20 * (100vw - 600px)/40)));
        height: 50px;
    }
<div id="square1"></div>
<div id="square2"></div>
<div id="square3"></div>
<div id="square4"></div>

Square 1 is for reference only.

Square 2 works somehow but only because I multiplied by factor 20 arbitrarily. Why does it work?

Square 3 and 4 shall avoid a horizontal overflow in case that the viewport is smaller than 600px. Both solutions don't work.

Link to Fiddle here

Any ideas? Thank you.

PS: I am no professional.


回答1:


The short answer to this question is:

/* for IE, Opera, Android and older browsers */
.rectangle { width: calc(55vw + 270px) }
@media (max-width:  600px) { .rectangle { width: 100% } }
@media (min-width: 1800px) { .rectangle { width:  70% } }

/* modern browsers */
.rectangle { width: max(70%, min(100%, calc(55vw + 270px))) }

To be able to use a 'Linear Equation' we need two points, p1(x1,y1) and p2(x2,y2), in an XY-space which depict a minimum and a maximum size at minimum and maximum viewport size.

Fortunately the OP gave us a few constraints:

  • viewport width <= 600px, element width 100%
  • viewport width >= 1800px, element width 70%
  • viewport width > 600px and < 1800px, element width calculated with linear equation

Using those constrainsts, we can define the required two points we need for the linear equation:

  • at viewport width 600px = x1 the element width is 100% (of 600px is 600px = y1)
  • at viewport width 1800px = x2 the element width is 70% (of 1800px is 1260px = y2)

We have two equations at our disposal:

  1. Y-intercept form: y = mx + b
  2. point slope form: y = y1 + m(x - x1)

(check out MathIsFun: Equation of a Straight Line, easy to understand Middle School explanations, well worth the read).

where

  • m = (y2 - y1) / (x2 - x1)

  • x = always defined as 100vmin,vw,vh or vmax depending on:

    • viewport width/height independent result (e.g. fontsize, padding, margin)
    • either viewport width or height dependent result (e.g. width, height, padding, margin)

  • b = y1 - m * x1 (see halfway page: https://mathforum.org/library/drmath/view/52848.html)

substituted

  1. y = (y2 - y1) / (x2 - x1) * x + (y - (y2 - y1) / (x2 - x1) * x1)
  2. y = y1 + (y2 - y1) / (x2 - x1) * (x - x1)

Fully substituted, 'point slope form' is the shortest, but to save on CPU load, I have opted to do some manual calculations and use the Y-intercept form in my final CSS calc().

By manually calculating 'm' and 'b' using points p1(600,600) and p2(1800,1260) we will yield the final equation we can use in CSS calc():

  • m = (1260 - 600) / (1800 - 600) = 0.55
  • b = 600 - 0.55 * 600 = 270
  • y = mx + b becomes: y = 0.55x + 270 (final equation)

width is in this case viewport width dependent, so we use viewport unit vw for 'x'

.rectangle { width: calc(0.55 * 100vw + 270px) } /* initially */
.rectangle { width: calc(55vw + 270px) }         /* simplified */

/* with min/max constraints */
.rectangle { width: max(70%, min(100%, calc(55vw + 270px))) }

The Snippet

var root      = document.documentElement;
var body      = document.body;
var rectangle = document.getElementById('demo');

// Polyfill FOR IE11, used for rounding
if (Number.EPSILON === undefined) { Number.EPSILON = Math.pow(2, -52); }

function updateSpecs() {
var txt = "<table><tbody>";
    txt += "<tr><td><b>#demo width/height<sup>*</sup></b>:" + "</td><td>" + rectangle.clientWidth + "/" + Math.round(((rectangle.clientWidth/root.clientWidth*100) + Number.EPSILON) * 1000) / 1000 + "%</td></tr>";
    txt += "<tr><td><br></tr>";
    txt += "<tr><td>Screen width/height:"        + "</td><td>" + screen.width       + "*" + screen.height      + "</td></tr>";
    txt += "<tr><td>window width/height:"        + "</td><td>" + window.innerWidth  + "*" + window.innerHeight + "</td></tr>";
    txt += "<tr><td><br></tr>";
    txt += "<tr><td>HTML width/height:"          + "</td><td>" + root.clientWidth   + "*" + root.clientHeight  + "</td></tr>";
    txt += "<tr><td>BODY width/height:"          + "</td><td>" + body.clientWidth   + "*" + body.clientHeight  + "</td></tr>";
    txt += "<tr><td><br></tr>";
    txt += "<tr><td colspan='2'><b><sup>*</sup></b>check width 600px and 1800px</tr>";
    txt += "</tbody></table>";

    document.getElementById("specs").innerHTML = txt;
}

updateSpecs() // first run

window.addEventListener('resize', updateSpecs);
/**************************/
/* preferred global rules */
/**************************/
html,body               { box-sizing: border-box; width: 100%; max-width: 100%; margin: 0 }
*::before,*::after, *   { box-sizing: inherit }

/* debugging output */
#specs { width: 100%; padding: 5rem; font-family: monospace }

/* rectangle eye-candy only */
.rectangle { background-color: purple; margin: 10px auto; height: 50px }

/* use of linear equation */
/* CSS for IE, Opera, Android and older browsers */
.rectangle { width: calc(55vw + 270px) } /* p1(600,600) p2(1800,1260) */
@media (max-width:  600px) { .rectangle { width: 100% } }
@media (min-width: 1800px) { .rectangle { width:  70% } }

/* CSS for modern browsers, no @media required */
#rectangle { width: max(70%, min(100%, calc(55vw + 270px))) }

/*
    NO MORE CSS BELOW THIS LINE, explanation and examples only
*/
/*
    LINEAR EQUATION, generic math
    math reference: https://www.mathsisfun.com/equation_of_line.html

    USING POINTS
        p1(x1,y1) - 1st point on an YX-graph => minimum viewport size, min required size limit 
        p2(x2,y2) - 2nd point on an YX-graph => maximum viewport size, max required size limit 

        parameter definition:
        p1(vp_minimum, size_at_vp_minimum)
        p2(vp_maximum, size_at_vp_maximum)

    WHERE
        x-axis: viewport size (either width or height of the browser window, device pixel, etc.)
        y-axis: required size (of font, width, height, padding, margin, etc.)

    CALCULATE
        y = required responsive size, the CSS calc() result

    WITH EITHER EQUATION
        1) point slope form: y - y1 = m(x - x1)
            simplified  y = y1 + m(x - x1)
            substituted y = y1 + (y2 - y1) / (x2 - x1) * (x - x1)

        2) y-intercept form: y = mx + b
            substituted y = (y2 - y1) / (x2 - x1) * x + (y1 - (y2 - y1) / (x2 - x1) * x1)

        where
            m = (y2 - y1) / (x2 - x1)

            x = always defined as 100vmin,vw,vh or vmax depending on:
                - viewport width/height independent result (e.g. fontsize, padding, margin)
                - either viewport width or height dependent result (e.g. width, height, padding, margin) 

            b = y1 - m * x1 (see halfway: http://mathforum.org/library/drmath/view/52848.html)

    RESULTING CSS 
        use either of six variations depending on
         - pre calculated values
         - SCSS pre-processor
         - CSS custom variables
         - CPU load

        vx = is either 100vmin,vw,vh or vmax

        1) point slope form
            a) calc( y1 + m * (100vx - x1) ) or
            b) calc( y1 + (y2 - y1) / (x2 - x1) * (100vx - x1) )

        2) y-intercept form
            a) calc( m * 100vx + b )
            b) calc( m * 100vx + (y1 - m * x1) )
            c) calc( (y2 - y1) / (x2 - x1) * 100vx + b )
            d) calc( (y2 - y1) / (x2 - x1) * 100vx + (y1 - (y2 - y1) / (x2 - x1) * x1) )

    NOTE: simplify 'mx' in (m * 100vx) by multiplying m * 100 and then use the vmin,vh,vw,vmax unit
          e.g. y = 0.01 * 100vw =>  y = 1vw  
*/

/* 
    LINEAR EQUATION, specific math for Stackoverflow question 54969190

    points p1(x1= 600,y1= 600) where x1 =  600px (min vp) and y1 =  600 = 100% of  600 (width at vp  600px)
           p2(x2=1800,y2=1260) where x2 = 1800px (max vp) and y2 = 1260 =  70% of 1800 (width at vp 1800px)

    Using y-intercept form 'y=mx+b' and manually calculating 'm' and 'b' our final equation will be

    m = (1260 - 600) / (1800 - 600) = 0.55
    b = 600 - 0.55 * 600 = 270
    y = 0.55x + 270

    'width' is in this case viewport width dependent, so use viewport unit VW for 'x'

    => CSS calc(0.55 * 100vw + 270px)
    => simplified calc(55vw + 270px)

    All below CSS calculation yield the same value for 'width'
*/
/* 1a) *//* width : max(70%, min(100%, calc(600px + 0.55 * (100vw - 600px))));/**/
/* 1b) *//* width : max(70%, min(100%, calc(600px + (1260 - 600) / (1800 - 600) * (100vw - 600px))));/**/
/* 2a) *//* width : max(70%, min(100%, calc(55vw + 270px))); /* preferred, least CPU intensive */
/* 2b) *//* width : max(70%, min(100%, calc(0.55 * 100vw + (600 - 0.55 * 600) * 1px)));/**/
/* 2c) *//* width : max(70%, min(100%, calc((1260 - 600) / (1800 - 600) * 100vw + 270px)));/**/
/* 2d) *//* width : max(70%, min(100%, calc((1260 - 600) / (1800 - 600) * 100vw + (600 - (1260 - 600) / (1800 - 600) * 600) * 1px)));/**/
<div id="demo" class="rectangle"></div>
<div id="specs"></div>


来源：https://stackoverflow.com/questions/54969190/responsive-fluid-design-using-linear-interpolation-for-layout

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responsive-design
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