Whārite Porowhita: Ariā, Āhua, me te Whakamahinga
Ko ngā porowhita he āhua ā-ira e kitea pinepinetia ana i roto i te oranga o ia rā, ahakoa he wira, he pereti, he hanganga rerekē rānei. I roto i te pāngarau, ko te porowhita te kohinga o ngā pūwāhi katoa i roto i te papa he tawhiti pumau mai i tētahi pūwāhi pumau e kiia nei ko te pokapū. Ko tēnei tawhiti pumau e mōhiotia ana ko te radius o te porowhita. I roto i tēnei tuhinga, ka matapakihia e tātou te whārite o te porowhita, mai i tōna ariā taketake me tōna āhua paerewa ki ōna tono mahi i te ao tūturu.
Ariā Taketake o ngā Porowhita
I mua i te ruku hohonu ki te whārite o te porowhita, he mea nui kia mārama ki ētahi ariā matua e pā ana ki ngā porowhita:
1. Pokapū o te Porowhita (O): Ko te pūwāhi pumau e ōrite ana te tawhiti o ngā pūwāhi katoa o te porowhita mai i reira.
2. Pūtoro (r): Te tawhiti pumau mai i te pokapū o te porowhita ki tētahi pūwāhi i runga i te porowhita.
3. Te whānui (d): He rārangi tika e tika ana mā waenganui o te porowhita, e hono ana i ngā pūwāhi e rua o te porowhita. Ko te roa o te whānui e rua te rahinga o te pūtoro, arā, \(d = 2r\).
Te Whārite o te Porowhita i roto i ngā Taunga Cartesian
Ka taea te whakaputa i te whārite o tētahi porowhita i roto i ngā taunga Cartesian i runga i te whakamāramatanga taketake o tētahi porowhita. Mehemea kei te pūwāhi \((h, k)\) te pokapū o te porowhita, ā, ko te radius ko \(r\). Kātahi, me tutuki i ia pūwāhi \((x, y)\) i runga i te porowhita te whārite e whai ake nei:
\[ \sqrt{(x – h)^2 + (y – k)^2} = r \]
Mā te tapawhā i ngā taha e rua o te whārite hei whakakore i te irahiko, ka whiwhi tātou:
\[ (x – h)^2 + (y – k)^2 = r^2 \]
Koinei te āhua whānui o te whārite o tētahi porowhita. Mēnā kei te pūtake (0, 0) te pokapū o te porowhita, ka māmā ake te whārite:
\[ x^2 + y^2 = r^2 \]
Ngā Huarahi Āhuahanga me te Tātari
He maha ngā wā ka whakamahia ngā huarahi āhuahanga hei tuhi me te mārama ki te āhua o te porowhita, engari i roto i te tātari pāngarau, he huarahi whai hua te whārite o te porowhita hei whakaoti rapanga. Hei tauira, hei whakatau i te tūranga o tētahi pūwāhi kua hoatu \((x_1, y_1)\) i runga i tētahi porowhita me te pokapū \((h, k)\) me te pūtoro \(r\), ka tirohia noa e mātou mēnā e tutuki ana te pūwāhi i te whārite o te porowhita:
\[ (x_1 – h)^2 + (y_1 – k)^2 = r^2 \]
Ki te tutuki te whārite, kei runga i te porowhita te pūwāhi. Ki te kore, kei waho, kei roto rānei i te porowhita te pūwāhi, i runga i tōna uara e pā ana ki te \(r^2\).
Te Hurihanga me te Nekehanga Porowhita
Ka taea te neke i ngā porowhita mā roto i ngā panonitanga āhuahanga, pērā i te nekehanga, te hurihanga, me te tauine. Mā te mārama ki te nekehanga, te whakarerekētanga rānei o te tūranga o ngā porowhita ka āwhina i a tātou i roto i ngā mahi maha. Hei tauira, ko te nekehanga o tētahi porowhita kua tautuhia e te pokapū \((h, k)\) ki tētahi pokapū hou \((h', k')\):
\[ x^2 + y^2 = r^2 \]
ka huri ki:
\[ (x – h')^2 + (y – k')^2 = r^2 \]
I roto i te horopaki o te hurihanga, ka mau tonu te āhua o te porowhita e huri ana i te pūtake, engari ka whai taunga hou ngā pūwāhi o te porowhita ka taea te tatau mā te whakamahi i te matihiko hurihanga.
Te Whakamahinga o te Whārite Porowhita
He maha ngā whakamahinga o te whārite porowhita i roto i ngā momo mara, mai i te hangarau me te ahupūngao ki te hoahoanga me te toi. Ko ētahi tauira o ēnei whakamahinga ko:
1. Hangarau me te Hoahoa Mīhini:
I roto i te mahi miihini, he maha ngā wāhanga mīhini pēnei i ngā camshaft, ngā taputapu, me ngā pūrei e hangaia ana i runga i te kaupapa o ngā porowhita. Ko te tātari i ō rātou nekehanga me ngā taunekeneke he maha ngā wā e hiahiatia ana te whakamahi i ngā whārite porowhita.
2. Te Tātaritanga whetū:
He maha ngā wā ka whakatatahia ngā porowhita o ngā aorangi me ngā amiorangi hei porowhita. I roto i tētahi tauira māmā, ka taea te whakaaro ko te porowhita o te aorangi he porowhita me te pokapū o te kaha ā-papatipu kei waenganui.
3. Te Mahere me te Āhua Whenua:
I roto i te mahere whenua, ka whakamahia ngā porowhita hei tautuhi i ngā rohe kua tuhia, kua whakawhāitihia hoki huri noa i tētahi wāhi. He mea whai hua tēnei hei whakatau i ngā tawhiti, ngā horahanga, me ngā rohe.
4. Whakairoiro Rorohiko me te Hoahoa:
I roto i ngā whakairoiro rorohiko me te hoahoa, ka whakamahia ngā porowhita me ngā pewa hei whakaatu i ngā momo taonga me ngā hanganga. Ko te rauropi a Bresenham tētahi rauropi rongonui mō te tuhi porowhita i runga i te mata rorohiko.
5. Toi me te Hanga Whare:
He maha ngā hoahoa whare e whakamahi ana i ngā porowhita, i ngā huānga porowhita rānei. Ko ngā tauira rongonui ko ngā matapihi rōhi o ngā whare karakia nui o te ao Kotiko me ngā tuanui o ngā whare tawhito maha.
Te Whakaoti Rapanga Mā te Whakamahi i ngā Whārite Porowhita
He maha ngā wā ka tūtaki tātou ki ngā raruraru e hiahia ana kia whakamahia te whārite o tētahi porowhita, pērā i te whakatau i te pūwāhi e whakawhiti ana i waenga i ngā porowhita e rua, i waenga rānei i tētahi porowhita me tētahi rārangi tika. Mō ngā porowhita e rua me ngā pokapū \((h_1, k_1)\) me \((h_2, k_2)\) me ngā radius \(r_1\) me \(r_2\) ia:
1. Whakakapia te whārite tuatahi ki te whārite tuarua hei whakakore i tētahi taurangi.
2. Whakamahia te pāngarau hei whakangawari me te kimi i ngā otinga mō ngā pūnaha whārite.
Mō tētahi rārangi e whakawhiti ana i tētahi porowhita, ka whakakapia te whārite o te rārangi \(y = mx + c\) ki roto i te whārite o te porowhita, ā, ka whakaotihia te whārite tapawhā e puta mai ana hei kimi i te pūwāhi whakawhiti.
Whakamutunga
He kaupapa matua te whārite o te porowhita i roto i te āhuahanga, e tuku ana i te whānuitanga o ngā tono mahi me ngā tono ariā. Mai i te hoahoa mīhini ki te toi, mai i te ahupūngao ki te mahere, ko te mārama ki te whārite o te porowhita me te pēhea te whakatinana i tēnei mea ka homai he taputapu whai hua ki a tātou hei whakaoti rapanga o ia rā. Mā te haere tonu ki te tūhura i tēnei ariā me te whakaharatau i tōna whakamahinga, ehara i te mea ka whānui ake i ō tātou tirohanga pāngarau engari ka whakarei ake hoki i ō tātou pūkenga tātari i roto i te whānuitanga o ngā tono.
