一旦我们得到角度和长度，我们需要单位化这些值：0.0到1.0。在27行，[```atan(y,x)```](../glossary/?search=atan) 会返回一个介于-PI到PI的弧度值（-3.14 to 3.14），所以我们要将这个返回值除以 ```TWO_PI```（在code顶部定义了）来得到一个-0.5到0.5的值。这样一来，用简单的加法就可以把这个返回值最终映射到0.0到1.0。半径会返回一个最大值0.5（因为我们计算的是到视口中心的距离，而视口中心的范围已经被映射到0.0到1.0），所以我们需要把这个值乘以二来得到一个0到1.0的映射。
@ -106,7 +106,7 @@ Das *HSB-Farbmodell* wurde ursprünglich entwickelt, um Farben in Polarkoordinat
Bei der Nutzung von Vektor- und Trigonometrie-Funktionen werden Variablen der Datentypen ```vec2```, ```vec3``` und ```vec4``` wie Vektoren behandelt, auch wenn sie tatsächlich Farben verkörpern. Wir beginnen hier also, Farben und Vektoren gleichermaßen zu bearbeiten - eine Flexibilität, die sich noch als äußerst praktisch und weitreichend erweisen wird.
**Hinweis:** Nur, falls Du Dich fragst: Abgesehen von [```length```](../glossary/?search=length) gibt es noch viele weitere geometrische Funktionen. Dazu gehören beisielsweise: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=fraceforward), [```reflect()```](../glossary/?search=reflect) und [```refract()```](../glossary/?search=refract).
**Hinweis:** Nur, falls Du Dich fragst: Abgesehen von [```length```](../glossary/?search=length) gibt es noch viele weitere geometrische Funktionen. Dazu gehören beisielsweise: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=faceforward), [```reflect()```](../glossary/?search=reflect) und [```refract()```](../glossary/?search=refract).
Außerdem bietet GLSL vergleichende Funktionen für Vektoren wie [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) und [```notEqual()```](../glossary/?search=notEqual).
@ -107,7 +107,7 @@ HSB fue originalmente diseñado para ser representado en coordenadas polares (ba
Cuando usamos vectores y funciones trigonométricas, ```vec2```, ```vec3``` y ```vec4``` son tratados como vectores, incluso cuando representan colores. Comenzaremos a tratar a los colores y a los vectores de una manera similar, de hecho te darás cuenta que es un concepto muy poderoso y flexible.
**Nota:** Si te preguntabas si había mas funciones geométricas además de [```length```](../glossary/?search=length): [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=fraceforward), [```reflect()```](../glossary/?search=reflect) y [```refract()```](../glossary/?search=refract). También GLSL tiene funciones relacionadas a los vectores como: [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) y [```notEqual()```](../glossary/?search=notEqual).
**Nota:** Si te preguntabas si había mas funciones geométricas además de [```length```](../glossary/?search=length): [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=faceforward), [```reflect()```](../glossary/?search=reflect) y [```refract()```](../glossary/?search=refract). También GLSL tiene funciones relacionadas a los vectores como: [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) y [```notEqual()```](../glossary/?search=notEqual).
Una vez que obtenemos el ángulo y la longitud, necesitamos "normalizar" sus valores al rango de 0.0 a 1.0. En la línea 27, [```atan(y,x)```](../glossary/?search=atan) devolverá el angulo en radianes entre -PI y PI (-3.14 a 3.14), por lo que necesitamos dividir este número por ```TWO_PI``` (declarado arriba en nuestro código) para obtener valores de -0.5 a 0.5, que con una simple suma podemos transformar al rango deseado de 0.0 a 1.0. El radio devolverá un máximo de 0.5 (porque estamos calculando la distancia desde el centro del viewport) por lo tanto necesitamos duplicar este rango (multiplicándolo por dos) para obtener un máximo de 1.0.
@ -215,7 +215,7 @@ Lorsqu'on utilise des vecteurs avec des fonctions trigonométriques les variable
Nous commencerons à traiter les couleurs et les vecteurs géométriques de façon similaire, en fait, vous devriez comprendre assez vite que cette flexibilité d'utilisation est une force.
**Note:** Si vous vous demandez s'il existe d'autres fonctions géométriques que [```length```](../glossary/?search=length)
comme: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=fraceforward), [```reflect()```](../glossary/?search=reflect) et [```refract()```](../glossary/?search=refract), la réponse est oui.
comme: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=faceforward), [```reflect()```](../glossary/?search=reflect) et [```refract()```](../glossary/?search=refract), la réponse est oui.
GLSL expose également des méthodes pour comparer les vecteurs entres eux: [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) et [```notEqual()```](../glossary/?search=notEqual).
Une fois que nous avons récupéré l'angle entre le centre et le fragment en cours, nous devons le normaliser.
@ -107,7 +107,7 @@ Originariamente HSB è stato creato per essere rappresentato in coordinate polar
Quando si usano vettori e funzioni trigonometriche, ```vec2```, ```vec3``` e ```vec4``` sono considerati come vettori anche quando rappresentano i colori. Inizieremo a considerare in modo simile i colori e i vettori, e in realtà troverete che questa flessibilità concettuale è molto potente.
**Nota:** se ve lo stavate chiedendo, esistono altre funzioni geometriche oltre a [```length```](../glossary/?search=length), come: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=fraceforward), [```reflect()```](../glossary/?search=reflect) e [```refract()```](../glossary/?search=refract). Anche GLSL ha speciali funzioni vettoriali come: [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) e [```notEqual()```](../glossary/?search=notEqual).
**Nota:** se ve lo stavate chiedendo, esistono altre funzioni geometriche oltre a [```length```](../glossary/?search=length), come: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=faceforward), [```reflect()```](../glossary/?search=reflect) e [```refract()```](../glossary/?search=refract). Anche GLSL ha speciali funzioni vettoriali come: [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) e [```notEqual()```](../glossary/?search=notEqual).
Una volta che otteniamo l'angolo e la lunghezza dobbiamo "normalizzare" i loro valori in una scala tra 0.0 e 1.0. alla riga 27, [```atan(y,x)```](../glossary/?search=atan) restituirà un angolo in radianti tra –PI e PI (-3.14 e 3.14), quindi dobbiamo dividere questo numero per ```TWO_PI``` (definito nella parte superiore del codice) per ottenere valori tra -0.5 e 0.5, che con una semplice addizione cambiamo nella scala desiderata tra 0.0 e 1.0. Il raggio restituirà un massimo di 0.5 (perché stiamo calcolando la distanza dal centro del punto di osservazione), quindi abbiamo bisogno di raddoppiare questa distanza (moltiplicando per due) per ottenere un massimo di 1.0.
@ -106,7 +106,7 @@ HSB was originally designed to be represented in polar coordinates (based on the
When using vector and trigonometric functions, ```vec2```, ```vec3``` and ```vec4``` are treated as vectors even when they represent colors. We will start treating colors and vectors similarly, in fact you will come to find this conceptual flexibility very empowering.
**Note:** If you were wondering, there are more geometric functions besides [```length```](../glossary/?search=length) like: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=fraceforward), [```reflect()```](../glossary/?search=reflect) and [```refract()```](../glossary/?search=refract). Also GLSL has special vector relational functions such as: [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) and [```notEqual()```](../glossary/?search=notEqual).
**Note:** If you were wondering, there are more geometric functions besides [```length```](../glossary/?search=length) like: [```distance()```](../glossary/?search=distance), [```dot()```](../glossary/?search=dot), [```cross```](../glossary/?search=cross), [```normalize()```](../glossary/?search=normalize), [```faceforward()```](../glossary/?search=faceforward), [```reflect()```](../glossary/?search=reflect) and [```refract()```](../glossary/?search=refract). Also GLSL has special vector relational functions such as: [```lessThan()```](../glossary/?search=lessThan), [```lessThanEqual()```](../glossary/?search=lessThanEqual), [```greaterThan()```](../glossary/?search=greaterThan), [```greaterThanEqual()```](../glossary/?search=greaterThanEqual), [```equal()```](../glossary/?search=equal) and [```notEqual()```](../glossary/?search=notEqual).
Once we obtain the angle and length we need to “normalize” their values to the range between 0.0 to 1.0. On line 27, [```atan(y,x)```](../glossary/?search=atan) will return an angle in radians between -PI and PI (-3.14 to 3.14), so we need to divide this number by ```TWO_PI``` (defined at the top of the code) to get values between -0.5 to 0.5, which by simple addition we change to the desired range of 0.0 to 1.0. The radius will return a maximum of 0.5 (because we are calculating the distance from the center of the viewport) so we need to double this range (by multiplying by two) to get a maximum of 1.0.
Michael Hadley
7 years ago